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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 3136.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3136.y1 | 3136z2 | \([0, -1, 0, -1633, -13887]\) | \(125000/49\) | \(188900999168\) | \([2]\) | \(3072\) | \(0.86233\) | |
| 3136.y2 | 3136z1 | \([0, -1, 0, 327, -1735]\) | \(8000/7\) | \(-3373232128\) | \([2]\) | \(1536\) | \(0.51575\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3136.y have rank \(1\).
Complex multiplication
The elliptic curves in class 3136.y do not have complex multiplication.Modular form 3136.2.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 LMFDB 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 LMFDB labels.
