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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 141570ey
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141570.s2 | 141570ey1 | \([1, -1, 0, 1207860, -14731938864]\) | \(4074304020054813/1962402098708480\) | \(-93865905658532525506560\) | \([]\) | \(13063680\) | \(3.0871\) | \(\Gamma_0(N)\)-optimal |
| 141570.s1 | 141570ey2 | \([1, -1, 0, -10872780, 398175477200]\) | \(-4076600308125723/1961812478912000\) | \(-68407685397882071182656000\) | \([]\) | \(39191040\) | \(3.6364\) |
Rank
sage: E.rank()
The elliptic curves in class 141570ey have rank \(0\).
Complex multiplication
The elliptic curves in class 141570ey do not have complex multiplication.Modular form 141570.2.a.ey
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
