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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 48400e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48400.q2 | 48400e1 | \([0, 1, 0, 11092, 10442188]\) | \(16/5\) | \(-47158953820000000\) | \([2]\) | \(304128\) | \(1.8785\) | \(\Gamma_0(N)\)-optimal |
| 48400.q1 | 48400e2 | \([0, 1, 0, -654408, 198113188]\) | \(821516/25\) | \(943179076400000000\) | \([2]\) | \(608256\) | \(2.2251\) |
Rank
sage: E.rank()
The elliptic curves in class 48400e have rank \(1\).
Complex multiplication
The elliptic curves in class 48400e do not have complex multiplication.Modular form 48400.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
