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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 363090r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363090.r1 | 363090r1 | \([1, 1, 0, -187303, 11369653]\) | \(6176938755473641/3093410611200\) | \(363936664997068800\) | \([2]\) | \(6193152\) | \(2.0624\) | \(\Gamma_0(N)\)-optimal |
363090.r2 | 363090r2 | \([1, 1, 0, 690777, 88465077]\) | \(309847571416194839/207860103360000\) | \(-24454533300200640000\) | \([2]\) | \(12386304\) | \(2.4090\) |
Rank
sage: E.rank()
The elliptic curves in class 363090r have rank \(1\).
Complex multiplication
The elliptic curves in class 363090r do not have complex multiplication.Modular form 363090.2.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.