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Properties

Label 56350h
Number of curves $2$
Conductor $56350$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 56350h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56350.c2 56350h1 \([1, 0, 1, -17176, -223002]\) \(304821217/164864\) \(303063824000000\) \([2]\) \(245760\) \(1.4698\) \(\Gamma_0(N)\)-optimal
56350.c1 56350h2 \([1, 0, 1, -213176, -37855002]\) \(582810602977/829472\) \(1524789864500000\) \([2]\) \(491520\) \(1.8163\)  

Rank

sage: E.rank()
 

The elliptic curves in class 56350h have rank \(2\).

Complex multiplication

The elliptic curves in class 56350h do not have complex multiplication.

Modular form 56350.2.a.h

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