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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 98736cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.e2 | 98736cb1 | \([0, -1, 0, 857608, -1502583696]\) | \(79448965607/1156415616\) | \(-1015349073578744610816\) | \([]\) | \(4257792\) | \(2.7115\) | \(\Gamma_0(N)\)-optimal |
| 98736.e1 | 98736cb2 | \([0, -1, 0, -7767272, 42022010736]\) | \(-59023897051273/834567929856\) | \(-732762306815666795053056\) | \([]\) | \(12773376\) | \(3.2608\) |
Rank
sage: E.rank()
The elliptic curves in class 98736cb have rank \(1\).
Complex multiplication
The elliptic curves in class 98736cb do not have complex multiplication.Modular form 98736.2.a.cb
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.
