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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 194633.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 194633.b1 | 194633b3 | \([1, -1, 0, -1038281, 407471520]\) | \(82483294977/17\) | \(25512415981433\) | \([2]\) | \(1229600\) | \(1.9598\) | |
| 194633.b2 | 194633b2 | \([1, -1, 0, -65116, 6332907]\) | \(20346417/289\) | \(433711071684361\) | \([2, 2]\) | \(614800\) | \(1.6132\) | |
| 194633.b3 | 194633b1 | \([1, -1, 0, -7871, -112880]\) | \(35937/17\) | \(25512415981433\) | \([2]\) | \(307400\) | \(1.2666\) | \(\Gamma_0(N)\)-optimal |
| 194633.b4 | 194633b4 | \([1, -1, 0, -7871, 17037722]\) | \(-35937/83521\) | \(-125342499716780329\) | \([2]\) | \(1229600\) | \(1.9598\) |
Rank
sage: E.rank()
The elliptic curves in class 194633.b have rank \(0\).
Complex multiplication
The elliptic curves in class 194633.b do not have complex multiplication.Modular form 194633.2.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 LMFDB 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 LMFDB labels.
