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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1936.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1936.b1 | 1936k2 | \([0, 1, 0, -58120, -5412684]\) | \(-24729001\) | \(-878013976576\) | \([]\) | \(4224\) | \(1.3741\) | |
1936.b2 | 1936k1 | \([0, 1, 0, -40, 372]\) | \(-121\) | \(-59969536\) | \([]\) | \(384\) | \(0.17519\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1936.b have rank \(1\).
Complex multiplication
The elliptic curves in class 1936.b do not have complex multiplication.Modular form 1936.2.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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.