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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 13050.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13050.bg1 | 13050bd2 | \([1, -1, 1, -1464980, 684851397]\) | \(-30526075007211889/103499257854\) | \(-1178921233993218750\) | \([]\) | \(219520\) | \(2.3317\) | |
| 13050.bg2 | 13050bd1 | \([1, -1, 1, -230, -462603]\) | \(-117649/8118144\) | \(-92470734000000\) | \([]\) | \(31360\) | \(1.3587\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13050.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 13050.bg do not have complex multiplication.Modular form 13050.2.a.bg
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
