Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 5520.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5520.b1 | 5520p4 | \([0, -1, 0, -6576, 206976]\) | \(7679186557489/20988075\) | \(85967155200\) | \([4]\) | \(10240\) | \(0.97147\) | |
5520.b2 | 5520p3 | \([0, -1, 0, -6096, -180480]\) | \(6117442271569/26953125\) | \(110400000000\) | \([2]\) | \(10240\) | \(0.97147\) | |
5520.b3 | 5520p2 | \([0, -1, 0, -576, 576]\) | \(5168743489/2975625\) | \(12188160000\) | \([2, 2]\) | \(5120\) | \(0.62490\) | |
5520.b4 | 5520p1 | \([0, -1, 0, 144, 0]\) | \(80062991/46575\) | \(-190771200\) | \([2]\) | \(2560\) | \(0.27832\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5520.b have rank \(1\).
Complex multiplication
The elliptic curves in class 5520.b do not have complex multiplication.Modular form 5520.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.