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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 98736ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.d2 | 98736ct1 | \([0, -1, 0, 7088, 1126336]\) | \(79448965607/1156415616\) | \(-573138081939456\) | \([]\) | \(387072\) | \(1.5125\) | \(\Gamma_0(N)\)-optimal |
| 98736.d1 | 98736ct2 | \([0, -1, 0, -64192, -31548416]\) | \(-59023897051273/834567929856\) | \(-413625219123511296\) | \([]\) | \(1161216\) | \(2.0618\) |
Rank
sage: E.rank()
The elliptic curves in class 98736ct have rank \(0\).
Complex multiplication
The elliptic curves in class 98736ct do not have complex multiplication.Modular form 98736.2.a.ct
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
