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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 2535.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2535.l1 | 2535m2 | \([1, 0, 1, -291698, 60610331]\) | \(258840217117/18225\) | \(193267001072925\) | \([2]\) | \(14976\) | \(1.7940\) | |
| 2535.l2 | 2535m1 | \([1, 0, 1, -17073, 1071631]\) | \(-51895117/16875\) | \(-178950926919375\) | \([2]\) | \(7488\) | \(1.4474\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2535.l have rank \(0\).
Complex multiplication
The elliptic curves in class 2535.l do not have complex multiplication.Modular form 2535.2.a.l
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.
