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SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 425880ff
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
425880.ff1 | 425880ff1 | \([0, 0, 0, -41067, 1542294]\) | \(78732/35\) | \(3405017962644480\) | \([2]\) | \(2211840\) | \(1.6759\) | \(\Gamma_0(N)\)-optimal |
425880.ff2 | 425880ff2 | \([0, 0, 0, 141453, 11507886]\) | \(1608714/1225\) | \(-238351257385113600\) | \([2]\) | \(4423680\) | \(2.0225\) |
Rank
sage: E.rank()
The elliptic curves in class 425880ff have rank \(1\).
Complex multiplication
The elliptic curves in class 425880ff do not have complex multiplication.Modular form 425880.2.a.ff
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.