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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 24882q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24882.p2 | 24882q1 | \([1, 0, 1, -1417796, 649667906]\) | \(-315184253425989830781625/1573946884992768\) | \(-1573946884992768\) | \([2]\) | \(350208\) | \(2.1148\) | \(\Gamma_0(N)\)-optimal |
24882.p1 | 24882q2 | \([1, 0, 1, -22684756, 41584312514]\) | \(1290999343784786961364509625/32193924048\) | \(32193924048\) | \([2]\) | \(700416\) | \(2.4613\) |
Rank
sage: E.rank()
The elliptic curves in class 24882q have rank \(0\).
Complex multiplication
The elliptic curves in class 24882q do not have complex multiplication.Modular form 24882.2.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 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.