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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 37200.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37200.r1 | 37200n2 | \([0, -1, 0, -368, 1632]\) | \(21587722/8649\) | \(2214144000\) | \([2]\) | \(17408\) | \(0.49127\) | |
37200.r2 | 37200n1 | \([0, -1, 0, -168, -768]\) | \(4121204/93\) | \(11904000\) | \([2]\) | \(8704\) | \(0.14469\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37200.r have rank \(1\).
Complex multiplication
The elliptic curves in class 37200.r do not have complex multiplication.Modular form 37200.2.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.