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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1935.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1935.b1 | 1935b2 | \([1, -1, 1, -83, -268]\) | \(2315685267/9245\) | \(249615\) | \([2]\) | \(256\) | \(-0.10759\) | |
1935.b2 | 1935b1 | \([1, -1, 1, -8, 2]\) | \(1860867/1075\) | \(29025\) | \([2]\) | \(128\) | \(-0.45417\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1935.b have rank \(1\).
Complex multiplication
The elliptic curves in class 1935.b do not have complex multiplication.Modular form 1935.2.a.b
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.