Properties

Label 17472i
Number of curves $3$
Conductor $17472$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 17472i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17472.c3 17472i1 \([0, -1, 0, 863, 92449]\) \(270840023/14329224\) \(-3756320096256\) \([]\) \(41472\) \(1.0926\) \(\Gamma_0(N)\)-optimal
17472.c2 17472i2 \([0, -1, 0, -7777, -2525471]\) \(-198461344537/10417365504\) \(-2730849862680576\) \([]\) \(124416\) \(1.6419\)  
17472.c1 17472i3 \([0, -1, 0, -1667617, -828339551]\) \(-1956469094246217097/36641439744\) \(-9605333580251136\) \([]\) \(373248\) \(2.1912\)  

Rank

sage: E.rank()
 

The elliptic curves in class 17472i have rank \(0\).

Complex multiplication

The elliptic curves in class 17472i do not have complex multiplication.

Modular form 17472.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} + q^{7} + q^{9} - 3 q^{11} - q^{13} + 3 q^{15} - 3 q^{17} + 7 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.