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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 7280f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7280.m1 | 7280f1 | \([0, 0, 0, -2747, 2746]\) | \(2238719766084/1292374265\) | \(1323391247360\) | \([2]\) | \(6912\) | \(1.0155\) | \(\Gamma_0(N)\)-optimal |
| 7280.m2 | 7280f2 | \([0, 0, 0, 10973, 21954]\) | \(71346044015118/41389887175\) | \(-84766488934400\) | \([2]\) | \(13824\) | \(1.3620\) |
Rank
sage: E.rank()
The elliptic curves in class 7280f have rank \(0\).
Complex multiplication
The elliptic curves in class 7280f do not have complex multiplication.Modular form 7280.2.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 Cremona 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 Cremona labels.
