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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 104040b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
104040.g2 | 104040b1 | \([0, 0, 0, -7803, 2387718]\) | \(-108/5\) | \(-2432510825610240\) | \([2]\) | \(491520\) | \(1.6323\) | \(\Gamma_0(N)\)-optimal |
104040.g1 | 104040b2 | \([0, 0, 0, -319923, 69243822]\) | \(3721734/25\) | \(24325108256102400\) | \([2]\) | \(983040\) | \(1.9789\) |
Rank
sage: E.rank()
The elliptic curves in class 104040b have rank \(1\).
Complex multiplication
The elliptic curves in class 104040b do not have complex multiplication.Modular form 104040.2.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 Cremona 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 Cremona labels.