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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 188760.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 188760.bd1 | 188760cc4 | \([0, -1, 0, -1006760, -388474260]\) | \(31103978031362/195\) | \(707490600960\) | \([2]\) | \(1966080\) | \(1.8793\) | |
| 188760.bd2 | 188760cc3 | \([0, -1, 0, -87160, -945140]\) | \(20183398562/11567205\) | \(41967634958346240\) | \([2]\) | \(1966080\) | \(1.8793\) | |
| 188760.bd3 | 188760cc2 | \([0, -1, 0, -62960, -6046500]\) | \(15214885924/38025\) | \(68980333593600\) | \([2, 2]\) | \(983040\) | \(1.5328\) | |
| 188760.bd4 | 188760cc1 | \([0, -1, 0, -2460, -165900]\) | \(-3631696/24375\) | \(-11054540640000\) | \([2]\) | \(491520\) | \(1.1862\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 188760.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 188760.bd do not have complex multiplication.Modular form 188760.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
