Show commands:
SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 24255be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24255.i4 | 24255be1 | \([1, -1, 1, -1553, -170544]\) | \(-4826809/144375\) | \(-12382483719375\) | \([2]\) | \(36864\) | \(1.1927\) | \(\Gamma_0(N)\)-optimal |
24255.i3 | 24255be2 | \([1, -1, 1, -56678, -5153844]\) | \(234770924809/1334025\) | \(114414149567025\) | \([2, 2]\) | \(73728\) | \(1.5393\) | |
24255.i2 | 24255be3 | \([1, -1, 1, -89753, 1580226]\) | \(932288503609/527295615\) | \(45224099518859415\) | \([2]\) | \(147456\) | \(1.8859\) | |
24255.i1 | 24255be4 | \([1, -1, 1, -905603, -331480614]\) | \(957681397954009/31185\) | \(2674616483385\) | \([2]\) | \(147456\) | \(1.8859\) |
Rank
sage: E.rank()
The elliptic curves in class 24255be have rank \(1\).
Complex multiplication
The elliptic curves in class 24255be do not have complex multiplication.Modular form 24255.2.a.be
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.