Properties

Label 7056.h
Number of curves $2$
Conductor $7056$
CM no
Rank $1$
Graph

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

Elliptic curves in class 7056.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.h1 7056bj2 \([0, 0, 0, -13419, -598374]\) \(-67645179/8\) \(-31603654656\) \([]\) \(10368\) \(1.0402\)  
7056.h2 7056bj1 \([0, 0, 0, 21, -2534]\) \(189/512\) \(-2774532096\) \([]\) \(3456\) \(0.49093\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7056.h have rank \(1\).

Complex multiplication

The elliptic curves in class 7056.h do not have complex multiplication.

Modular form 7056.2.a.h

sage: E.q_eigenform(10)
 
\(q - 3q^{5} + 3q^{11} - 2q^{13} - 6q^{17} + 2q^{19} + O(q^{20})\)  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.