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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 35739.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35739.q1 | 35739c1 | \([1, -1, 0, -45012, -3316005]\) | \(1157625/121\) | \(1054220708643993\) | \([2]\) | \(164160\) | \(1.6176\) | \(\Gamma_0(N)\)-optimal |
35739.q2 | 35739c2 | \([1, -1, 0, 57873, -16341246]\) | \(2460375/14641\) | \(-127560705745923153\) | \([2]\) | \(328320\) | \(1.9642\) |
Rank
sage: E.rank()
The elliptic curves in class 35739.q have rank \(1\).
Complex multiplication
The elliptic curves in class 35739.q do not have complex multiplication.Modular form 35739.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.