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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 6864.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6864.w1 | 6864v2 | \([0, 1, 0, -208, -940]\) | \(244140625/61347\) | \(251277312\) | \([2]\) | \(2048\) | \(0.32178\) | |
| 6864.w2 | 6864v1 | \([0, 1, 0, 32, -76]\) | \(857375/1287\) | \(-5271552\) | \([2]\) | \(1024\) | \(-0.024791\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6864.w have rank \(0\).
Complex multiplication
The elliptic curves in class 6864.w do not have complex multiplication.Modular form 6864.2.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 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.
