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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 10830.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10830.l1 | 10830j2 | \([1, 0, 1, -1316214, 581105836]\) | \(781484460931/900\) | \(290418928001100\) | \([2]\) | \(145920\) | \(2.0592\) | |
10830.l2 | 10830j1 | \([1, 0, 1, -81594, 9229852]\) | \(-186169411/6480\) | \(-2091016281607920\) | \([2]\) | \(72960\) | \(1.7126\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10830.l have rank \(0\).
Complex multiplication
The elliptic curves in class 10830.l do not have complex multiplication.Modular form 10830.2.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.