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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 6864.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6864.p1 | 6864l2 | \([0, -1, 0, -976, 11968]\) | \(25128011089/245388\) | \(1005109248\) | \([2]\) | \(7680\) | \(0.54678\) | |
| 6864.p2 | 6864l1 | \([0, -1, 0, -16, 448]\) | \(-117649/20592\) | \(-84344832\) | \([2]\) | \(3840\) | \(0.20020\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6864.p have rank \(0\).
Complex multiplication
The elliptic curves in class 6864.p do not have complex multiplication.Modular form 6864.2.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 LMFDB 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 LMFDB labels.
