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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 350064p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350064.p1 | 350064p1 | \([0, 0, 0, -1791, -29026]\) | \(91919306736/537251\) | \(3713478912\) | \([2]\) | \(180224\) | \(0.67679\) | \(\Gamma_0(N)\)-optimal |
| 350064.p2 | 350064p2 | \([0, 0, 0, -771, -61870]\) | \(-1833256044/58749977\) | \(-1624319364096\) | \([2]\) | \(360448\) | \(1.0234\) |
Rank
sage: E.rank()
The elliptic curves in class 350064p have rank \(0\).
Complex multiplication
The elliptic curves in class 350064p do not have complex multiplication.Modular form 350064.2.a.p
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.
