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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 9680.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9680.q1 | 9680h3 | \([0, 0, 0, -12947, -567006]\) | \(132304644/5\) | \(9070392320\) | \([2]\) | \(10240\) | \(0.99673\) | |
9680.q2 | 9680h2 | \([0, 0, 0, -847, -7986]\) | \(148176/25\) | \(11337990400\) | \([2, 2]\) | \(5120\) | \(0.65016\) | |
9680.q3 | 9680h1 | \([0, 0, 0, -242, 1331]\) | \(55296/5\) | \(141724880\) | \([2]\) | \(2560\) | \(0.30359\) | \(\Gamma_0(N)\)-optimal |
9680.q4 | 9680h4 | \([0, 0, 0, 1573, -45254]\) | \(237276/625\) | \(-1133799040000\) | \([2]\) | \(10240\) | \(0.99673\) |
Rank
sage: E.rank()
The elliptic curves in class 9680.q have rank \(1\).
Complex multiplication
The elliptic curves in class 9680.q do not have complex multiplication.Modular form 9680.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.