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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 15246.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15246.bk1 | 15246bf4 | \([1, -1, 1, -15390860, -23234858215]\) | \(312196988566716625/25367712678\) | \(32761588370432210982\) | \([2]\) | \(552960\) | \(2.7898\) | |
| 15246.bk2 | 15246bf3 | \([1, -1, 1, -896270, -414575719]\) | \(-61653281712625/21875235228\) | \(-28251165611302411932\) | \([2]\) | \(276480\) | \(2.4432\) | |
| 15246.bk3 | 15246bf2 | \([1, -1, 1, -395330, 48083753]\) | \(5290763640625/2291573592\) | \(2959493892674274648\) | \([2]\) | \(184320\) | \(2.2405\) | |
| 15246.bk4 | 15246bf1 | \([1, -1, 1, 83830, 5534345]\) | \(50447927375/39517632\) | \(-51035755938729408\) | \([2]\) | \(92160\) | \(1.8939\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15246.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 15246.bk do not have complex multiplication.Modular form 15246.2.a.bk
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
