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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 112700y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 112700.ba2 | 112700y1 | \([0, -1, 0, 32667, 2093162]\) | \(1048576/1127\) | \(-4143450718750000\) | \([2]\) | \(691200\) | \(1.6833\) | \(\Gamma_0(N)\)-optimal |
| 112700.ba1 | 112700y2 | \([0, -1, 0, -181708, 19671912]\) | \(11279504/3703\) | \(217827123500000000\) | \([2]\) | \(1382400\) | \(2.0299\) |
Rank
sage: E.rank()
The elliptic curves in class 112700y have rank \(0\).
Complex multiplication
The elliptic curves in class 112700y do not have complex multiplication.Modular form 112700.2.a.y
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.
