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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 3675.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3675.b1 | 3675f2 | \([0, -1, 1, -10208, 410318]\) | \(-102400/3\) | \(-3446748046875\) | \([]\) | \(9900\) | \(1.1846\) | |
3675.b2 | 3675f1 | \([0, -1, 1, 82, -1282]\) | \(20480/243\) | \(-714717675\) | \([]\) | \(1980\) | \(0.37986\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3675.b have rank \(0\).
Complex multiplication
The elliptic curves in class 3675.b do not have complex multiplication.Modular form 3675.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.