Properties

Label 5880.p
Number of curves $4$
Conductor $5880$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 5880.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5880.p1 5880g4 \([0, -1, 0, -10600, 423340]\) \(546718898/405\) \(97582786560\) \([2]\) \(9216\) \(1.0424\)  
5880.p2 5880g3 \([0, -1, 0, -6680, -205428]\) \(136835858/1875\) \(451772160000\) \([2]\) \(9216\) \(1.0424\)  
5880.p3 5880g2 \([0, -1, 0, -800, 3900]\) \(470596/225\) \(27106329600\) \([2, 2]\) \(4608\) \(0.69578\)  
5880.p4 5880g1 \([0, -1, 0, 180, 372]\) \(21296/15\) \(-451772160\) \([2]\) \(2304\) \(0.34921\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5880.p have rank \(1\).

Complex multiplication

The elliptic curves in class 5880.p do not have complex multiplication.

Modular form 5880.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} + 6 q^{13} - q^{15} + 2 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.