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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 102245b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102245.j4 | 102245b1 | \([1, -1, 0, 16615, -643824]\) | \(59319/55\) | \(-470304261836695\) | \([2]\) | \(276480\) | \(1.5026\) | \(\Gamma_0(N)\)-optimal |
| 102245.j3 | 102245b2 | \([1, -1, 0, -85630, -5735625]\) | \(8120601/3025\) | \(25866734401018225\) | \([2, 2]\) | \(552960\) | \(1.8492\) | |
| 102245.j2 | 102245b3 | \([1, -1, 0, -596855, 173499860]\) | \(2749884201/73205\) | \(625974972504641045\) | \([2]\) | \(1105920\) | \(2.1958\) | |
| 102245.j1 | 102245b4 | \([1, -1, 0, -1210325, -512073314]\) | \(22930509321/6875\) | \(58788032729586875\) | \([2]\) | \(1105920\) | \(2.1958\) |
Rank
sage: E.rank()
The elliptic curves in class 102245b have rank \(0\).
Complex multiplication
The elliptic curves in class 102245b do not have complex multiplication.Modular form 102245.2.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.
