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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 97020.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97020.l1 | 97020a1 | \([0, 0, 0, -84040488, 296538415012]\) | \(-1647408715474378752/3025\) | \(-120535071148800\) | \([3]\) | \(4499712\) | \(2.8484\) | \(\Gamma_0(N)\)-optimal |
97020.l2 | 97020a2 | \([0, 0, 0, -83793528, 298367823348]\) | \(-2239956387422208/27680640625\) | \(-804066030629190252000000\) | \([]\) | \(13499136\) | \(3.3977\) |
Rank
sage: E.rank()
The elliptic curves in class 97020.l have rank \(0\).
Complex multiplication
The elliptic curves in class 97020.l do not have complex multiplication.Modular form 97020.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.