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Properties

Label 57434h
Number of curves $2$
Conductor $57434$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 57434h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57434.e2 57434h1 \([1, -1, 1, -5937, -267807]\) \(-2146689/1664\) \(-17936614307456\) \([]\) \(196420\) \(1.2419\) \(\Gamma_0(N)\)-optimal
57434.e1 57434h2 \([1, -1, 1, -469827, 136115853]\) \(-1064019559329/125497034\) \(-1352759552636834186\) \([]\) \(1374940\) \(2.2149\)  

Rank

sage: E.rank()
 

The elliptic curves in class 57434h have rank \(0\).

Complex multiplication

The elliptic curves in class 57434h do not have complex multiplication.

Modular form 57434.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} + q^{5} - 3 q^{6} + q^{7} + q^{8} + 6 q^{9} + q^{10} + 2 q^{11} - 3 q^{12} + q^{13} + q^{14} - 3 q^{15} + q^{16} - 3 q^{17} + 6 q^{18} - 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.