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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 2704.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2704.n1 | 2704j2 | \([0, 0, 0, -575107, 184183298]\) | \(-1064019559329/125497034\) | \(-2481152873203736576\) | \([]\) | \(56448\) | \(2.2654\) | |
| 2704.n2 | 2704j1 | \([0, 0, 0, -7267, -364702]\) | \(-2146689/1664\) | \(-32898294480896\) | \([]\) | \(8064\) | \(1.2925\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2704.n have rank \(0\).
Complex multiplication
The elliptic curves in class 2704.n do not have complex multiplication.Modular form 2704.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
