Properties

Label 208080.m
Number of curves $4$
Conductor $208080$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 208080.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
208080.m1 208080br4 \([0, 0, 0, -272211123, -1728626305678]\) \(30949975477232209/478125000\) \(34460570029478400000000\) \([2]\) \(42467328\) \(3.4596\)  
208080.m2 208080br2 \([0, 0, 0, -17521203, -25311058702]\) \(8253429989329/936360000\) \(67487580345730498560000\) \([2, 2]\) \(21233664\) \(3.1130\)  
208080.m3 208080br1 \([0, 0, 0, -4204083, 2897264882]\) \(114013572049/15667200\) \(1129203958725948211200\) \([2]\) \(10616832\) \(2.7664\) \(\Gamma_0(N)\)-optimal
208080.m4 208080br3 \([0, 0, 0, 24094797, -127328521102]\) \(21464092074671/109596256200\) \(-7899083841566026203955200\) \([2]\) \(42467328\) \(3.4596\)  

Rank

sage: E.rank()
 

The elliptic curves in class 208080.m have rank \(1\).

Complex multiplication

The elliptic curves in class 208080.m do not have complex multiplication.

Modular form 208080.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4 q^{7} + 4 q^{11} - 2 q^{13} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.