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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 97344eq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97344.cy2 | 97344eq1 | \([0, 0, 0, -499395, 135757024]\) | \(61162984000/41067\) | \(9248272002111168\) | \([2]\) | \(860160\) | \(2.0020\) | \(\Gamma_0(N)\)-optimal |
| 97344.cy1 | 97344eq2 | \([0, 0, 0, -598260, 78178048]\) | \(1643032000/767637\) | \(11063778936679452672\) | \([2]\) | \(1720320\) | \(2.3486\) |
Rank
sage: E.rank()
The elliptic curves in class 97344eq have rank \(1\).
Complex multiplication
The elliptic curves in class 97344eq do not have complex multiplication.Modular form 97344.2.a.eq
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.
