Properties

Label 7056.m
Number of curves $2$
Conductor $7056$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.m1 7056bw2 \([0, 0, 0, -131376, 18343024]\) \(-1713910976512/1594323\) \(-233270525472768\) \([]\) \(24960\) \(1.6798\)  
7056.m2 7056bw1 \([0, 0, 0, -336, -2576]\) \(-28672/3\) \(-438939648\) \([]\) \(1920\) \(0.39737\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7056.m have rank \(0\).

Complex multiplication

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

Modular form 7056.2.a.m

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

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.