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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 257400j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257400.j2 | 257400j1 | \([0, 0, 0, 19725, 98750]\) | \(72765788/42471\) | \(-495381744000000\) | \([2]\) | \(983040\) | \(1.5091\) | \(\Gamma_0(N)\)-optimal |
257400.j1 | 257400j2 | \([0, 0, 0, -79275, 791750]\) | \(2361864386/1355211\) | \(31614362208000000\) | \([2]\) | \(1966080\) | \(1.8557\) |
Rank
sage: E.rank()
The elliptic curves in class 257400j have rank \(2\).
Complex multiplication
The elliptic curves in class 257400j do not have complex multiplication.Modular form 257400.2.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 Cremona 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 Cremona labels.