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Properties

Label 56350.h
Number of curves $2$
Conductor $56350$
CM no
Rank $1$
Graph

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

Elliptic curves in class 56350.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56350.h1 56350u1 \([1, 0, 1, -376, -4602]\) \(-7649089/7360\) \(-5635000000\) \([]\) \(51840\) \(0.56717\) \(\Gamma_0(N)\)-optimal
56350.h2 56350u2 \([1, 0, 1, 3124, 79398]\) \(4405959551/6083500\) \(-4657679687500\) \([]\) \(155520\) \(1.1165\)  

Rank

sage: E.rank()
 

The elliptic curves in class 56350.h have rank \(1\).

Complex multiplication

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

Modular form 56350.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.