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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 375347.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
375347.b1 | 375347b2 | \([1, 0, 0, -285709, -58804236]\) | \(408023180713/1421\) | \(8982656892629\) | \([2]\) | \(1951488\) | \(1.7050\) | |
375347.b2 | 375347b1 | \([1, 0, 0, -17604, -947177]\) | \(-95443993/5887\) | \(-37213864269463\) | \([2]\) | \(975744\) | \(1.3584\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 375347.b have rank \(1\).
Complex multiplication
The elliptic curves in class 375347.b do not have complex multiplication.Modular form 375347.2.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.