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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 439569.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 439569.t1 | 439569t1 | \([1, -1, 1, -10119245, -8673373276]\) | \(274625/81\) | \(33799708394878640102577\) | \([2]\) | \(30081024\) | \(3.0287\) | \(\Gamma_0(N)\)-optimal |
| 439569.t2 | 439569t2 | \([1, -1, 1, 27244120, -57813670924]\) | \(5359375/6561\) | \(-2737776379985169848308737\) | \([2]\) | \(60162048\) | \(3.3752\) |
Rank
sage: E.rank()
The elliptic curves in class 439569.t have rank \(0\).
Complex multiplication
The elliptic curves in class 439569.t do not have complex multiplication.Modular form 439569.2.a.t
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.
