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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 45864w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 45864.cc1 | 45864w1 | \([0, 0, 0, -287238, 55667185]\) | \(1909913257984/129730653\) | \(178023918121712208\) | \([2]\) | \(737280\) | \(2.0586\) | \(\Gamma_0(N)\)-optimal |
| 45864.cc2 | 45864w2 | \([0, 0, 0, 248577, 239451730]\) | \(77366117936/1172914587\) | \(-25752661604174598912\) | \([2]\) | \(1474560\) | \(2.4052\) |
Rank
sage: E.rank()
The elliptic curves in class 45864w have rank \(0\).
Complex multiplication
The elliptic curves in class 45864w do not have complex multiplication.Modular form 45864.2.a.w
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.
