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SageMath
E = EllipticCurve("fk1")
E.isogeny_class()
Elliptic curves in class 101430fk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.ej2 | 101430fk1 | \([1, -1, 1, -5522, -284371]\) | \(-217081801/285660\) | \(-24499950124860\) | \([2]\) | \(331776\) | \(1.2620\) | \(\Gamma_0(N)\)-optimal |
101430.ej1 | 101430fk2 | \([1, -1, 1, -106952, -13429699]\) | \(1577505447721/838350\) | \(71902027540350\) | \([2]\) | \(663552\) | \(1.6086\) |
Rank
sage: E.rank()
The elliptic curves in class 101430fk have rank \(0\).
Complex multiplication
The elliptic curves in class 101430fk do not have complex multiplication.Modular form 101430.2.a.fk
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.