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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1083b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1083.a3 | 1083b1 | \([1, 1, 1, -549, 4050]\) | \(389017/57\) | \(2681615217\) | \([4]\) | \(540\) | \(0.53406\) | \(\Gamma_0(N)\)-optimal |
| 1083.a2 | 1083b2 | \([1, 1, 1, -2354, -40714]\) | \(30664297/3249\) | \(152852067369\) | \([2, 2]\) | \(1080\) | \(0.88064\) | |
| 1083.a1 | 1083b3 | \([1, 1, 1, -36649, -2715724]\) | \(115714886617/1539\) | \(72403610859\) | \([2]\) | \(2160\) | \(1.2272\) | |
| 1083.a4 | 1083b4 | \([1, 1, 1, 3061, -194500]\) | \(67419143/390963\) | \(-18393198773403\) | \([2]\) | \(2160\) | \(1.2272\) |
Rank
sage: E.rank()
The elliptic curves in class 1083b have rank \(0\).
Complex multiplication
The elliptic curves in class 1083b do not have complex multiplication.Modular form 1083.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
