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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 258570.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
258570.j1 | 258570j2 | \([1, -1, 0, -70260345, -226643906579]\) | \(10901014250685308569/1040774054400\) | \(3662217210530674598400\) | \([2]\) | \(34836480\) | \(3.1744\) | |
258570.j2 | 258570j1 | \([1, -1, 0, -4066425, -4086708755]\) | \(-2113364608155289/828431400960\) | \(-2915037823544489410560\) | \([2]\) | \(17418240\) | \(2.8278\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 258570.j have rank \(0\).
Complex multiplication
The elliptic curves in class 258570.j do not have complex multiplication.Modular form 258570.2.a.j
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.