Properties

Label 331200.hw
Number of curves $4$
Conductor $331200$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("hw1")
 
E.isogeny_class()
 

Elliptic curves in class 331200.hw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
331200.hw1 331200hw3 \([0, 0, 0, -950700, 351106000]\) \(63649751618/1164375\) \(1738402560000000000\) \([2]\) \(4718592\) \(2.2948\)  
331200.hw2 331200hw2 \([0, 0, 0, -122700, -8246000]\) \(273671716/119025\) \(88851686400000000\) \([2, 2]\) \(2359296\) \(1.9483\)  
331200.hw3 331200hw1 \([0, 0, 0, -104700, -13034000]\) \(680136784/345\) \(64385280000000\) \([2]\) \(1179648\) \(1.6017\) \(\Gamma_0(N)\)-optimal
331200.hw4 331200hw4 \([0, 0, 0, 417300, -61166000]\) \(5382838942/4197615\) \(-6267005614080000000\) \([2]\) \(4718592\) \(2.2948\)  

Rank

sage: E.rank()
 

The elliptic curves in class 331200.hw have rank \(2\).

Complex multiplication

The elliptic curves in class 331200.hw do not have complex multiplication.

Modular form 331200.2.a.hw

sage: E.q_eigenform(10)
 
\(q - 4 q^{11} + 2 q^{13} + 2 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.