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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 9675.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9675.v1 | 9675b2 | \([1, -1, 0, -2067, -35534]\) | \(2315685267/9245\) | \(3900234375\) | \([2]\) | \(6144\) | \(0.69713\) | |
9675.v2 | 9675b1 | \([1, -1, 0, -192, 91]\) | \(1860867/1075\) | \(453515625\) | \([2]\) | \(3072\) | \(0.35055\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9675.v have rank \(0\).
Complex multiplication
The elliptic curves in class 9675.v do not have complex multiplication.Modular form 9675.2.a.v
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.