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Properties

Label 37338q
Number of curves $2$
Conductor $37338$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 37338q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37338.n2 37338q1 \([1, 1, 1, -4995355, -4258844311]\) \(117174888570509216929/1273887851544576\) \(149871631846367821824\) \([]\) \(1397088\) \(2.6865\) \(\Gamma_0(N)\)-optimal
37338.n1 37338q2 \([1, 1, 1, -1095694195, 13959438182969]\) \(1236526859255318155975783969/38367061931916216\) \(4513846469228010896184\) \([]\) \(9779616\) \(3.6594\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37338q have rank \(0\).

Complex multiplication

The elliptic curves in class 37338q do not have complex multiplication.

Modular form 37338.2.a.q

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.