Properties

Label 3960.h
Number of curves 22
Conductor 39603960
CM no
Rank 11
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 3960.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3960.h1 3960m1 [0,0,0,2403,45198][0, 0, 0, -2403, 45198] 76136652/27576136652/275 55427328005542732800 [2][2] 38403840 0.730760.73076 Γ0(N)\Gamma_0(N)-optimal
3960.h2 3960m2 [0,0,0,1323,86022][0, 0, 0, -1323, 86022] 6353046/75625-6353046/75625 3048503040000-3048503040000 [2][2] 76807680 1.07731.0773  

Rank

sage: E.rank()
 

The elliptic curves in class 3960.h have rank 11.

Complex multiplication

The elliptic curves in class 3960.h do not have complex multiplication.

Modular form 3960.2.a.h

sage: E.q_eigenform(10)
 
qq5+4q7+q114q13+2q176q19+O(q20)q - q^{5} + 4 q^{7} + q^{11} - 4 q^{13} + 2 q^{17} - 6 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the LMFDB numbering.

(1221)\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.