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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 443760.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443760.b1 | 443760b1 | \([0, -1, 0, -1775656, -859679744]\) | \(1203052/75\) | \(38599112596749542400\) | \([2]\) | \(9687040\) | \(2.5097\) | \(\Gamma_0(N)\)-optimal |
443760.b2 | 443760b2 | \([0, -1, 0, 1404624, -3604897440]\) | \(297754/5625\) | \(-5789866889512431360000\) | \([2]\) | \(19374080\) | \(2.8563\) |
Rank
sage: E.rank()
The elliptic curves in class 443760.b have rank \(1\).
Complex multiplication
The elliptic curves in class 443760.b do not have complex multiplication.Modular form 443760.2.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.