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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 9075.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9075.c1 | 9075i2 | \([1, 1, 1, -283, 1706]\) | \(15069223/81\) | \(13476375\) | \([2]\) | \(3072\) | \(0.21209\) | |
9075.c2 | 9075i1 | \([1, 1, 1, -8, 56]\) | \(-343/9\) | \(-1497375\) | \([2]\) | \(1536\) | \(-0.13448\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9075.c have rank \(2\).
Complex multiplication
The elliptic curves in class 9075.c do not have complex multiplication.Modular form 9075.2.a.c
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.