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Properties

Label 343230.l
Number of curves $2$
Conductor $343230$
CM no
Rank $0$
Graph

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

Elliptic curves in class 343230.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
343230.l1 343230l2 \([1, 0, 0, -16943009365, -848857250127235]\) \(-537892346392757834815139433407447761/63783099740879053154940\) \(-63783099740879053154940\) \([]\) \(337446144\) \(4.2405\)  
343230.l2 343230l1 \([1, 0, 0, 14097935, -37071642775]\) \(309877627207229469173251439/773065454327965440000000\) \(-773065454327965440000000\) \([7]\) \(48206592\) \(3.2676\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 343230.l have rank \(0\).

Complex multiplication

The elliptic curves in class 343230.l do not have complex multiplication.

Modular form 343230.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} + q^{14} + q^{15} + q^{16} + q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.