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SageMath
E = EllipticCurve("jb1")
E.isogeny_class()
Elliptic curves in class 310464.jb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 310464.jb1 | 310464jb2 | \([0, 0, 0, -14700, -642096]\) | \(1687500/121\) | \(25189369970688\) | \([2]\) | \(737280\) | \(1.3183\) | |
| 310464.jb2 | 310464jb1 | \([0, 0, 0, -2940, 49392]\) | \(54000/11\) | \(572485681152\) | \([2]\) | \(368640\) | \(0.97171\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 310464.jb have rank \(2\).
Complex multiplication
The elliptic curves in class 310464.jb do not have complex multiplication.Modular form 310464.2.a.jb
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
