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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 193116.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193116.l1 | 193116bd2 | \([0, -1, 0, -177668, 20271000]\) | \(1367595682000/402300927\) | \(182451361929484032\) | \([2]\) | \(2419200\) | \(2.0179\) | |
193116.l2 | 193116bd1 | \([0, -1, 0, 29847, 2092686]\) | \(103737344000/127413867\) | \(-3611543002182192\) | \([2]\) | \(1209600\) | \(1.6714\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 193116.l have rank \(0\).
Complex multiplication
The elliptic curves in class 193116.l do not have complex multiplication.Modular form 193116.2.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.