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SageMath
E = EllipticCurve("m1")
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)
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.