Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 24882j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24882.b3 | 24882j1 | \([1, 1, 0, -754468121, 7976132108901]\) | \(47494836285140078125125156832537/9270904211712\) | \(9270904211712\) | \([2]\) | \(4587520\) | \(3.2777\) | \(\Gamma_0(N)\)-optimal |
24882.b2 | 24882j2 | \([1, 1, 0, -754468201, 7976130332725]\) | \(47494851393481427423717280072217/20983804907895336942864\) | \(20983804907895336942864\) | \([2, 2]\) | \(9175040\) | \(3.6243\) | |
24882.b4 | 24882j3 | \([1, 1, 0, -750662821, 8060575520305]\) | \(-46779807755660187695380243787737/998813488693913841955545396\) | \(-998813488693913841955545396\) | \([4]\) | \(18350080\) | \(3.9709\) | |
24882.b1 | 24882j4 | \([1, 1, 0, -758274861, 7891571471481]\) | \(48217388775148129472035202597977/997806266020361242131115572\) | \(997806266020361242131115572\) | \([2]\) | \(18350080\) | \(3.9709\) |
Rank
sage: E.rank()
The elliptic curves in class 24882j have rank \(0\).
Complex multiplication
The elliptic curves in class 24882j do not have complex multiplication.Modular form 24882.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.