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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 71478.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 71478.f1 | 71478w2 | \([1, -1, 0, -1040688, -114925824]\) | \(24928563670864867/13279961395712\) | \(66402609050414495232\) | \([2]\) | \(1900800\) | \(2.4949\) | |
| 71478.f2 | 71478w1 | \([1, -1, 0, -602928, 178986240]\) | \(4847659921191907/42218553344\) | \(211101674834755584\) | \([2]\) | \(950400\) | \(2.1483\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 71478.f have rank \(1\).
Complex multiplication
The elliptic curves in class 71478.f do not have complex multiplication.Modular form 71478.2.a.f
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.
