Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 309442d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
309442.d2 | 309442d1 | \([1, -1, 0, -2298892, 1342183548]\) | \(1513942435265625/459172\) | \(407516840212132\) | \([2]\) | \(3563520\) | \(2.1672\) | \(\Gamma_0(N)\)-optimal |
309442.d1 | 309442d2 | \([1, -1, 0, -2308502, 1330403610]\) | \(1533007996997625/26354865698\) | \(23390040319235634338\) | \([2]\) | \(7127040\) | \(2.5138\) |
Rank
sage: E.rank()
The elliptic curves in class 309442d have rank \(1\).
Complex multiplication
The elliptic curves in class 309442d do not have complex multiplication.Modular form 309442.2.a.d
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.