Properties

Label 334620.l
Number of curves $4$
Conductor $334620$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 334620.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
334620.l1 334620l4 \([0, 0, 0, -380244423, 2853923928622]\) \(6749703004355978704/5671875\) \(5109215940972000000\) \([2]\) \(31850496\) \(3.3253\)  
334620.l2 334620l3 \([0, 0, 0, -23760048, 44613162997]\) \(-26348629355659264/24169921875\) \(-1360764188824218750000\) \([2]\) \(15925248\) \(2.9788\)  
334620.l3 334620l2 \([0, 0, 0, -4800783, 3728076118]\) \(13584145739344/1195803675\) \(1077178040521503148800\) \([2]\) \(10616832\) \(2.7760\)  
334620.l4 334620l1 \([0, 0, 0, 332592, 271261393]\) \(72268906496/606436875\) \(-34142335525545390000\) \([2]\) \(5308416\) \(2.4295\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 334620.l have rank \(2\).

Complex multiplication

The elliptic curves in class 334620.l do not have complex multiplication.

Modular form 334620.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2q^{7} + q^{11} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.