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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 3675q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3675.q1 | 3675q1 | \([0, 1, 1, -408, 3119]\) | \(-102400/3\) | \(-220591875\) | \([]\) | \(1980\) | \(0.37986\) | \(\Gamma_0(N)\)-optimal |
3675.q2 | 3675q2 | \([0, 1, 1, 2042, -156131]\) | \(20480/243\) | \(-11167463671875\) | \([]\) | \(9900\) | \(1.1846\) |
Rank
sage: E.rank()
The elliptic curves in class 3675q have rank \(0\).
Complex multiplication
The elliptic curves in class 3675q do not have complex multiplication.Modular form 3675.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.