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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 35904r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35904.m1 | 35904r1 | \([0, -1, 0, -6729, -210231]\) | \(8227727284672/5049\) | \(20680704\) | \([2]\) | \(27648\) | \(0.72515\) | \(\Gamma_0(N)\)-optimal |
| 35904.m2 | 35904r2 | \([0, -1, 0, -6689, -212895]\) | \(-1010234719304/25492401\) | \(-835334995968\) | \([2]\) | \(55296\) | \(1.0717\) |
Rank
sage: E.rank()
The elliptic curves in class 35904r have rank \(0\).
Complex multiplication
The elliptic curves in class 35904r do not have complex multiplication.Modular form 35904.2.a.r
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.
