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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 3330.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3330.r1 | 3330m2 | \([1, -1, 1, -409598, -100796019]\) | \(281470209323873024547/35046400\) | \(946252800\) | \([2]\) | \(28160\) | \(1.5838\) | |
3330.r2 | 3330m1 | \([1, -1, 1, -25598, -1570419]\) | \(-68700855708416547/24248320000\) | \(-654704640000\) | \([2]\) | \(14080\) | \(1.2372\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3330.r have rank \(0\).
Complex multiplication
The elliptic curves in class 3330.r do not have complex multiplication.Modular form 3330.2.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 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.