↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 309738d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
309738.d2 309738d1 \([1, 1, 0, 4686, 276876]\) \(241804367/833976\) \(-39235135652856\) \([]\) \(1710720\) \(1.2914\) \(\Gamma_0(N)\)-optimal
309738.d1 309738d2 \([1, 1, 0, -222744, 40441014]\) \(-25979045828113/52635726\) \(-2476294101744606\) \([]\) \(5132160\) \(1.8407\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 309738.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 3 q^{5} + q^{6} + 5 q^{7} - q^{8} + q^{9} + 3 q^{10} - q^{11} - q^{12} - q^{13} - 5 q^{14} + 3 q^{15} + q^{16} - q^{18} + O(q^{20})\) 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.