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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 990.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
990.l1 | 990l1 | \([1, -1, 1, -797, -8539]\) | \(-76711450249/851840\) | \(-620991360\) | \([]\) | \(840\) | \(0.50212\) | \(\Gamma_0(N)\)-optimal |
990.l2 | 990l2 | \([1, -1, 1, 2668, -45961]\) | \(2882081488391/2883584000\) | \(-2102132736000\) | \([3]\) | \(2520\) | \(1.0514\) |
Rank
sage: E.rank()
The elliptic curves in class 990.l have rank \(0\).
Complex multiplication
The elliptic curves in class 990.l do not have complex multiplication.Modular form 990.2.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.