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Properties

Label 336350ca
Number of curves $2$
Conductor $336350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 336350ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
336350.ca2 336350ca1 \([1, 1, 1, 107612, -11355219]\) \(397535/392\) \(-135899001153125000\) \([]\) \(3628800\) \(1.9745\) \(\Gamma_0(N)\)-optimal
336350.ca1 336350ca2 \([1, 1, 1, -1093638, 618099781]\) \(-417267265/235298\) \(-81573375442163281250\) \([]\) \(10886400\) \(2.5238\)  

Rank

sage: E.rank()
 

The elliptic curves in class 336350ca have rank \(1\).

Complex multiplication

The elliptic curves in class 336350ca do not have complex multiplication.

Modular form 336350.2.a.ca

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} - 2 q^{9} - 3 q^{11} - q^{12} - 2 q^{13} + q^{14} + q^{16} - 3 q^{17} - 2 q^{18} - 7 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.