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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 338130.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338130.x1 | 338130x1 | \([1, -1, 0, -2187495, 1245661821]\) | \(65787589563409/10400000\) | \(183001393130400000\) | \([2]\) | \(9830400\) | \(2.3229\) | \(\Gamma_0(N)\)-optimal |
338130.x2 | 338130x2 | \([1, -1, 0, -1979415, 1491986925]\) | \(-48743122863889/26406250000\) | \(-464651974745156250000\) | \([2]\) | \(19660800\) | \(2.6694\) |
Rank
sage: E.rank()
The elliptic curves in class 338130.x have rank \(0\).
Complex multiplication
The elliptic curves in class 338130.x do not have complex multiplication.Modular form 338130.2.a.x
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.