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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 48400.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48400.bd1 | 48400cz3 | \([0, -1, 0, -1467876208, 21646998590912]\) | \(-24680042791780949/369098752\) | \(-5231047633534976000000000\) | \([]\) | \(17280000\) | \(3.8799\) | |
| 48400.bd2 | 48400cz1 | \([0, -1, 0, -1356208, -608049088]\) | \(-19465109/22\) | \(-311794736000000000\) | \([]\) | \(691200\) | \(2.2705\) | \(\Gamma_0(N)\)-optimal |
| 48400.bd3 | 48400cz2 | \([0, -1, 0, 9533792, 6376070912]\) | \(6761990971/5153632\) | \(-73039787676416000000000\) | \([]\) | \(3456000\) | \(3.0752\) |
Rank
sage: E.rank()
The elliptic curves in class 48400.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 48400.bd do not have complex multiplication.Modular form 48400.2.a.bd
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.
\(\left(\begin{array}{rrr} 1 & 25 & 5 \\ 25 & 1 & 5 \\ 5 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
