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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 493680l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.l2 | 493680l1 | \([0, -1, 0, 559464, -335733264]\) | \(2005142581/6196500\) | \(-59846749664385024000\) | \([2]\) | \(10948608\) | \(2.4781\) | \(\Gamma_0(N)\)-optimal* |
493680.l1 | 493680l2 | \([0, -1, 0, -5190456, -3905283600]\) | \(1601202365099/243843750\) | \(2355080426607744000000\) | \([2]\) | \(21897216\) | \(2.8247\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 493680l have rank \(0\).
Complex multiplication
The elliptic curves in class 493680l do not have complex multiplication.Modular form 493680.2.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 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.