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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 466752.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466752.l1 | 466752l2 | \([0, -1, 0, -33489, -2347695]\) | \(253526452425808/4091373\) | \(67033055232\) | \([2]\) | \(950272\) | \(1.2100\) | \(\Gamma_0(N)\)-optimal* |
466752.l2 | 466752l1 | \([0, -1, 0, -2029, -38531]\) | \(-902576293888/126190779\) | \(-129219357696\) | \([2]\) | \(475136\) | \(0.86346\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 466752.l have rank \(0\).
Complex multiplication
The elliptic curves in class 466752.l do not have complex multiplication.Modular form 466752.2.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.