Show commands:
SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 24150.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24150.bq1 | 24150bo4 | \([1, 1, 1, -37912263, -89430033219]\) | \(385693937170561837203625/2159357734550274048\) | \(33739964602348032000000\) | \([2]\) | \(4147200\) | \(3.1651\) | |
| 24150.bq2 | 24150bo2 | \([1, 1, 1, -2799888, 1716931281]\) | \(155355156733986861625/8291568305839392\) | \(129555754778740500000\) | \([2]\) | \(1382400\) | \(2.6158\) | |
| 24150.bq3 | 24150bo3 | \([1, 1, 1, -1048263, -2947089219]\) | \(-8152944444844179625/235342826399858688\) | \(-3677231662497792000000\) | \([2]\) | \(2073600\) | \(2.8185\) | |
| 24150.bq4 | 24150bo1 | \([1, 1, 1, 116112, 107299281]\) | \(11079872671250375/324440155855872\) | \(-5069377435248000000\) | \([2]\) | \(691200\) | \(2.2692\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24150.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 24150.bq do not have complex multiplication.Modular form 24150.2.a.bq
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
