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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 283746bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 283746.bg4 | 283746bg1 | \([1, 0, 0, -10657, -64183]\) | \(2845178713/1609728\) | \(75731071930368\) | \([2]\) | \(870912\) | \(1.3532\) | \(\Gamma_0(N)\)-optimal |
| 283746.bg2 | 283746bg2 | \([1, 0, 0, -126177, -17230455]\) | \(4722184089433/9884736\) | \(465036113572416\) | \([2, 2]\) | \(1741824\) | \(1.6997\) | |
| 283746.bg3 | 283746bg3 | \([1, 0, 0, -82857, -29230095]\) | \(-1337180541913/7067998104\) | \(-332520197709009624\) | \([2]\) | \(3483648\) | \(2.0463\) | |
| 283746.bg1 | 283746bg4 | \([1, 0, 0, -2017817, -1103410143]\) | \(19312898130234073/84888\) | \(3993630746328\) | \([2]\) | \(3483648\) | \(2.0463\) |
Rank
sage: E.rank()
The elliptic curves in class 283746bg have rank \(1\).
Complex multiplication
The elliptic curves in class 283746bg do not have complex multiplication.Modular form 283746.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
