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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 18150.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18150.q1 | 18150j2 | \([1, 1, 0, -1387025, 694047765]\) | \(-6663170841705625/850403524608\) | \(-37663542961451827200\) | \([]\) | \(570240\) | \(2.4900\) | |
18150.q2 | 18150j1 | \([1, 1, 0, 110350, -2111820]\) | \(3355354844375/1987172352\) | \(-88009925977036800\) | \([]\) | \(190080\) | \(1.9407\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18150.q have rank \(0\).
Complex multiplication
The elliptic curves in class 18150.q do not have complex multiplication.Modular form 18150.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.