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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 9075.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9075.r1 | 9075q2 | \([1, 0, 1, -7076, 227423]\) | \(15069223/81\) | \(210568359375\) | \([2]\) | \(15360\) | \(1.0168\) | |
9075.r2 | 9075q1 | \([1, 0, 1, -201, 7423]\) | \(-343/9\) | \(-23396484375\) | \([2]\) | \(7680\) | \(0.67023\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9075.r have rank \(1\).
Complex multiplication
The elliptic curves in class 9075.r do not have complex multiplication.Modular form 9075.2.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.