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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 48139.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48139.l1 | 48139e1 | \([0, 1, 1, -23110599, -42770385080]\) | \(-9221261135586623488/121324931\) | \(-17960444018448659\) | \([]\) | \(1824768\) | \(2.6773\) | \(\Gamma_0(N)\)-optimal |
48139.l2 | 48139e2 | \([0, 1, 1, -21803969, -47818398791]\) | \(-7743965038771437568/2189290237869371\) | \(-324093526642013801855819\) | \([]\) | \(5474304\) | \(3.2266\) |
Rank
sage: E.rank()
The elliptic curves in class 48139.l have rank \(1\).
Complex multiplication
The elliptic curves in class 48139.l do not have complex multiplication.Modular form 48139.2.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.