Properties

Label 137280.fi
Number of curves $8$
Conductor $137280$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fi1")
 
E.isogeny_class()
 

Elliptic curves in class 137280.fi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
137280.fi1 137280bs8 \([0, 1, 0, -67008001, 118677373439]\) \(126929854754212758768001/50235797102795981820\) \(13169012795715349858222080\) \([2]\) \(31850496\) \(3.5184\)  
137280.fi2 137280bs6 \([0, 1, 0, -58489601, 172099667199]\) \(84415028961834287121601/30783551683856400\) \(8069723372612852121600\) \([2, 2]\) \(15925248\) \(3.1718\)  
137280.fi3 137280bs3 \([0, 1, 0, -58484481, 172131318015]\) \(84392862605474684114881/11228954880\) \(2943603148062720\) \([2]\) \(7962624\) \(2.8252\)  
137280.fi4 137280bs7 \([0, 1, 0, -50053121, 223496390655]\) \(-52902632853833942200321/51713453577420277500\) \(-13556371574599261224960000\) \([2]\) \(31850496\) \(3.5184\)  
137280.fi5 137280bs5 \([0, 1, 0, -30201601, -63887865601]\) \(11621808143080380273601/1335706803288000\) \(350147524241129472000\) \([2]\) \(10616832\) \(2.9691\)  
137280.fi6 137280bs2 \([0, 1, 0, -2041601, -826361601]\) \(3590017885052913601/954068544000000\) \(250103344398336000000\) \([2, 2]\) \(5308416\) \(2.6225\)  
137280.fi7 137280bs1 \([0, 1, 0, -730881, 229816575]\) \(164711681450297281/8097103872000\) \(2122607197421568000\) \([2]\) \(2654208\) \(2.2759\) \(\Gamma_0(N)\)-optimal
137280.fi8 137280bs4 \([0, 1, 0, 5146879, -5339289345]\) \(57519563401957999679/80296734375000000\) \(-21049307136000000000000\) \([2]\) \(10616832\) \(2.9691\)  

Rank

sage: E.rank()
 

The elliptic curves in class 137280.fi have rank \(1\).

Complex multiplication

The elliptic curves in class 137280.fi do not have complex multiplication.

Modular form 137280.2.a.fi

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 4 q^{7} + q^{9} - q^{11} - q^{13} - q^{15} - 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 3 & 6 & 12 & 12 \\ 2 & 1 & 2 & 2 & 6 & 3 & 6 & 6 \\ 4 & 2 & 1 & 4 & 12 & 6 & 3 & 12 \\ 4 & 2 & 4 & 1 & 12 & 6 & 12 & 3 \\ 3 & 6 & 12 & 12 & 1 & 2 & 4 & 4 \\ 6 & 3 & 6 & 6 & 2 & 1 & 2 & 2 \\ 12 & 6 & 3 & 12 & 4 & 2 & 1 & 4 \\ 12 & 6 & 12 & 3 & 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.