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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 23184.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23184.bb1 | 23184bn4 | \([0, 0, 0, -218374635, -1236062404582]\) | \(385693937170561837203625/2159357734550274048\) | \(6447807645643365502943232\) | \([2]\) | \(5529600\) | \(3.6028\) | |
| 23184.bb2 | 23184bn2 | \([0, 0, 0, -16127355, 23750985386]\) | \(155355156733986861625/8291568305839392\) | \(24758490296143531081728\) | \([2]\) | \(1843200\) | \(3.0535\) | |
| 23184.bb3 | 23184bn3 | \([0, 0, 0, -6037995, -40734523366]\) | \(-8152944444844179625/235342826399858688\) | \(-702729914144755644628992\) | \([2]\) | \(2764800\) | \(3.2562\) | |
| 23184.bb4 | 23184bn1 | \([0, 0, 0, 668805, 1482636458]\) | \(11079872671250375/324440155855872\) | \(-968773114343140098048\) | \([2]\) | \(921600\) | \(2.7069\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23184.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 23184.bb do not have complex multiplication.Modular form 23184.2.a.bb
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.
