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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 41280d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41280.s4 | 41280d1 | \([0, -1, 0, -6881, 67425]\) | \(137467988281/72562500\) | \(19021824000000\) | \([2]\) | \(92160\) | \(1.2396\) | \(\Gamma_0(N)\)-optimal |
| 41280.s3 | 41280d2 | \([0, -1, 0, -86881, 9875425]\) | \(276670733768281/336980250\) | \(88337350656000\) | \([2]\) | \(184320\) | \(1.5862\) | |
| 41280.s2 | 41280d3 | \([0, -1, 0, -318881, -69201375]\) | \(13679527032530281/381633600\) | \(100042958438400\) | \([2]\) | \(276480\) | \(1.7889\) | |
| 41280.s1 | 41280d4 | \([0, -1, 0, -331681, -63331295]\) | \(15393836938735081/2275690697640\) | \(596558662242140160\) | \([2]\) | \(552960\) | \(2.1355\) |
Rank
sage: E.rank()
The elliptic curves in class 41280d have rank \(1\).
Complex multiplication
The elliptic curves in class 41280d do not have complex multiplication.Modular form 41280.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
