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Properties

Label 309738j
Number of curves $2$
Conductor $309738$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 309738j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
309738.j2 309738j1 \([1, 1, 0, 50, -68]\) \(37109375/30888\) \(-11150568\) \([]\) \(69984\) \(0.039964\) \(\Gamma_0(N)\)-optimal
309738.j1 309738j2 \([1, 1, 0, -520, 5746]\) \(-43204686625/17545242\) \(-6333832362\) \([]\) \(209952\) \(0.58927\)  

Rank

sage: E.rank()
 

The elliptic curves in class 309738j have rank \(0\).

Complex multiplication

The elliptic curves in class 309738j do not have complex multiplication.

Modular form 309738.2.a.j

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