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Properties

Label 56550h
Number of curves $2$
Conductor $56550$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 56550h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.a1 56550h1 \([1, 1, 0, -47625, -3922875]\) \(764579942079121/21285239040\) \(332581860000000\) \([2]\) \(331776\) \(1.5658\) \(\Gamma_0(N)\)-optimal
56550.a2 56550h2 \([1, 1, 0, 10375, -12796875]\) \(7903193128559/4535269736400\) \(-70863589631250000\) \([2]\) \(663552\) \(1.9124\)  

Rank

sage: E.rank()
 

The elliptic curves in class 56550h have rank \(2\).

Complex multiplication

The elliptic curves in class 56550h do not have complex multiplication.

Modular form 56550.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 4 q^{7} - q^{8} + q^{9} - 4 q^{11} - q^{12} + q^{13} + 4 q^{14} + q^{16} - 4 q^{17} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.