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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 1350.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1350.q1 | 1350t2 | \([1, -1, 1, -1805, 30197]\) | \(-6847995/64\) | \(-6075000000\) | \([3]\) | \(1080\) | \(0.69899\) | |
1350.q2 | 1350t1 | \([1, -1, 1, 70, 197]\) | \(3645/4\) | \(-42187500\) | \([]\) | \(360\) | \(0.14969\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1350.q have rank \(0\).
Complex multiplication
The elliptic curves in class 1350.q do not have complex multiplication.Modular form 1350.2.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.