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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 24990x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24990.u2 | 24990x1 | \([1, 0, 1, -17029, -877348]\) | \(-13532315887/382500\) | \(-15435254677500\) | \([2]\) | \(100352\) | \(1.3108\) | \(\Gamma_0(N)\)-optimal |
24990.u1 | 24990x2 | \([1, 0, 1, -274279, -55311448]\) | \(56547934727887/43350\) | \(1749328863450\) | \([2]\) | \(200704\) | \(1.6573\) |
Rank
sage: E.rank()
The elliptic curves in class 24990x have rank \(1\).
Complex multiplication
The elliptic curves in class 24990x do not have complex multiplication.Modular form 24990.2.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 Cremona 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 Cremona labels.