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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 810.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
810.b1 | 810d1 | \([1, -1, 0, -24, 80]\) | \(-2146689/2000\) | \(-1458000\) | \([3]\) | \(144\) | \(-0.12077\) | \(\Gamma_0(N)\)-optimal |
810.b2 | 810d2 | \([1, -1, 0, 201, -1315]\) | \(15166431/20480\) | \(-1209323520\) | \([]\) | \(432\) | \(0.42854\) |
Rank
sage: E.rank()
The elliptic curves in class 810.b have rank \(1\).
Complex multiplication
The elliptic curves in class 810.b do not have complex multiplication.Modular form 810.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.