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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 116032.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116032.t1 | 116032l1 | \([0, 0, 0, -3308872, 2316690600]\) | \(33256413948450816/2481997\) | \(299012572214272\) | \([2]\) | \(1880064\) | \(2.2273\) | \(\Gamma_0(N)\)-optimal |
| 116032.t2 | 116032l2 | \([0, 0, 0, -3302012, 2326774800]\) | \(-2065624967846736/17960084863\) | \(-34619163017987473408\) | \([2]\) | \(3760128\) | \(2.5738\) |
Rank
sage: E.rank()
The elliptic curves in class 116032.t have rank \(1\).
Complex multiplication
The elliptic curves in class 116032.t do not have complex multiplication.Modular form 116032.2.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.
