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Properties

Label 338130s
Number of curves $2$
Conductor $338130$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 338130s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
338130.s2 338130s1 \([1, -1, 0, -236745, -9569219]\) \(16974593/9360\) \(809177260004689680\) \([2]\) \(4456448\) \(2.1268\) \(\Gamma_0(N)\)-optimal
338130.s1 338130s2 \([1, -1, 0, -2889765, -1887376775]\) \(30870492353/50700\) \(4383043491692069100\) \([2]\) \(8912896\) \(2.4734\)  

Rank

sage: E.rank()
 

The elliptic curves in class 338130s have rank \(1\).

Complex multiplication

The elliptic curves in class 338130s do not have complex multiplication.

Modular form 338130.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + 4 q^{11} + q^{13} + q^{16} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.