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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 10350.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10350.q1 | 10350g2 | \([1, -1, 0, -24012, 922576]\) | \(84013940106985/28705554432\) | \(523158729523200\) | \([]\) | \(41472\) | \(1.5263\) | |
10350.q2 | 10350g1 | \([1, -1, 0, -9837, -373019]\) | \(5776556465785/1073088\) | \(19557028800\) | \([]\) | \(13824\) | \(0.97696\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10350.q have rank \(0\).
Complex multiplication
The elliptic curves in class 10350.q do not have complex multiplication.Modular form 10350.2.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.