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SageMath
E = EllipticCurve("ez1")
E.isogeny_class()
Elliptic curves in class 46800ez
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.fl2 | 46800ez1 | \([0, 0, 0, -32032875, -69781243750]\) | \(623295446073461/5458752\) | \(31835441664000000000\) | \([2]\) | \(2949120\) | \(2.9091\) | \(\Gamma_0(N)\)-optimal |
| 46800.fl1 | 46800ez2 | \([0, 0, 0, -32752875, -66480043750]\) | \(666276475992821/58199166792\) | \(339417540730944000000000\) | \([2]\) | \(5898240\) | \(3.2557\) |
Rank
sage: E.rank()
The elliptic curves in class 46800ez have rank \(0\).
Complex multiplication
The elliptic curves in class 46800ez do not have complex multiplication.Modular form 46800.2.a.ez
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.
