Properties

Label 3360.h
Number of curves $4$
Conductor $3360$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 3360.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3360.h1 3360q3 \([0, -1, 0, -102060000, 396888659352]\) \(229625675762164624948320008/9568125\) \(4898880000\) \([2]\) \(215040\) \(2.7600\)  
3360.h2 3360q2 \([0, -1, 0, -6400625, 6158314977]\) \(7079962908642659949376/100085966990454375\) \(409952120792901120000\) \([2]\) \(215040\) \(2.7600\)  
3360.h3 3360q1 \([0, -1, 0, -6378750, 6202979352]\) \(448487713888272974160064/91549016015625\) \(5859137025000000\) \([2, 2]\) \(107520\) \(2.4134\) \(\Gamma_0(N)\)-optimal
3360.h4 3360q4 \([0, -1, 0, -6356880, 6247602900]\) \(-55486311952875723077768/801237030029296875\) \(-410233359375000000000\) \([4]\) \(215040\) \(2.7600\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3360.h have rank \(0\).

Complex multiplication

The elliptic curves in class 3360.h do not have complex multiplication.

Modular form 3360.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} - 4q^{11} - 6q^{13} - q^{15} + 6q^{17} - 4q^{19} + O(q^{20})\)  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.