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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 338130.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338130.t1 | 338130t1 | \([1, -1, 0, -13722930, -14998822700]\) | \(3305951312273/788486400\) | \(68165092382795058643200\) | \([2]\) | \(46792704\) | \(3.0927\) | \(\Gamma_0(N)\)-optimal |
338130.t2 | 338130t2 | \([1, -1, 0, 32262750, -94084995164]\) | \(42959580557167/69087330000\) | \(-5972638503252115114290000\) | \([2]\) | \(93585408\) | \(3.4393\) |
Rank
sage: E.rank()
The elliptic curves in class 338130.t have rank \(1\).
Complex multiplication
The elliptic curves in class 338130.t do not have complex multiplication.Modular form 338130.2.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 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.