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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 66924p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66924.q2 | 66924p1 | \([0, 0, 0, 137904, 8972548]\) | \(321978368/224939\) | \(-202624691931028224\) | \([]\) | \(604800\) | \(2.0094\) | \(\Gamma_0(N)\)-optimal |
| 66924.q1 | 66924p2 | \([0, 0, 0, -2539056, 1592394388]\) | \(-2009615368192/53094899\) | \(-47827800216876835584\) | \([]\) | \(1814400\) | \(2.5587\) |
Rank
sage: E.rank()
The elliptic curves in class 66924p have rank \(0\).
Complex multiplication
The elliptic curves in class 66924p do not have complex multiplication.Modular form 66924.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
