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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 7056.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7056.n1 | 7056bv2 | \([0, 0, 0, -19551, -974806]\) | \(109744/9\) | \(67778563974912\) | \([2]\) | \(21504\) | \(1.3965\) | |
| 7056.n2 | 7056bv1 | \([0, 0, 0, -4116, 84035]\) | \(16384/3\) | \(1412053416144\) | \([2]\) | \(10752\) | \(1.0499\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7056.n have rank \(0\).
Complex multiplication
The elliptic curves in class 7056.n do not have complex multiplication.Modular form 7056.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
