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SageMath
E = EllipticCurve("ox1")
E.isogeny_class()
Elliptic curves in class 235200.ox
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.ox1 | 235200ox2 | \([0, 1, 0, -1099233, 468974463]\) | \(-7620530425/526848\) | \(-10155317715271680000\) | \([]\) | \(5971968\) | \(2.3980\) | |
| 235200.ox2 | 235200ox1 | \([0, 1, 0, 76767, 691263]\) | \(2595575/1512\) | \(-29144725585920000\) | \([]\) | \(1990656\) | \(1.8487\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235200.ox have rank \(2\).
Complex multiplication
The elliptic curves in class 235200.ox do not have complex multiplication.Modular form 235200.2.a.ox
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
