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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 83490t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83490.v2 | 83490t1 | \([1, 0, 1, -509, 10712]\) | \(-120188964049/343388160\) | \(-41549967360\) | \([]\) | \(89856\) | \(0.72460\) | \(\Gamma_0(N)\)-optimal |
83490.v1 | 83490t2 | \([1, 0, 1, -55949, 5089016]\) | \(-160067871234233809/219006000\) | \(-26499726000\) | \([]\) | \(269568\) | \(1.2739\) |
Rank
sage: E.rank()
The elliptic curves in class 83490t have rank \(1\).
Complex multiplication
The elliptic curves in class 83490t do not have complex multiplication.Modular form 83490.2.a.t
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 Cremona 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 Cremona labels.