Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.g1 7056bn2 \([0, 0, 0, -102459, -12687766]\) \(-16591834777/98304\) \(-704775544897536\) \([]\) \(34560\) \(1.6894\)  
7056.g2 7056bn1 \([0, 0, 0, 3381, -92806]\) \(596183/864\) \(-6194316312576\) \([]\) \(11520\) \(1.1401\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7056.2.a.g

sage: E.q_eigenform(10)
 
\(q - 3q^{5} + 3q^{11} - 4q^{13} + 4q^{19} + O(q^{20})\)  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.