Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 305760.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
305760.v1 | 305760v4 | \([0, -1, 0, -11148496, -14319428780]\) | \(2543984126301795848/909361981125\) | \(54776590191296064000\) | \([2]\) | \(14155776\) | \(2.7567\) | |
305760.v2 | 305760v2 | \([0, -1, 0, -5758496, 5211309720]\) | \(350584567631475848/8259273550125\) | \(497507980236111936000\) | \([2]\) | \(14155776\) | \(2.7567\) | |
305760.v3 | 305760v1 | \([0, -1, 0, -797246, -154778280]\) | \(7442744143086784/2927948765625\) | \(22046095636929000000\) | \([2, 2]\) | \(7077888\) | \(2.4102\) | \(\Gamma_0(N)\)-optimal |
305760.v4 | 305760v3 | \([0, -1, 0, 2556559, -1120003359]\) | \(3834800837445824/3342041015625\) | \(-1610497161000000000000\) | \([2]\) | \(14155776\) | \(2.7567\) |
Rank
sage: E.rank()
The elliptic curves in class 305760.v have rank \(1\).
Complex multiplication
The elliptic curves in class 305760.v do not have complex multiplication.Modular form 305760.2.a.v
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.