↑

Properties

Label 350.a
Number of curves $2$
Conductor $350$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 350.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350.a1 350c2 \([1, 1, 0, -45, -185]\) \(-417267265/235298\) \(-5882450\) \([]\) \(72\) \(0.0021345\)  
350.a2 350c1 \([1, 1, 0, 5, 5]\) \(397535/392\) \(-9800\) \([]\) \(24\) \(-0.54717\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 350.a have rank \(1\).

Complex multiplication

The elliptic curves in class 350.a do not have complex multiplication.

Modular form 350.2.a.a

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 LMFDB 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 LMFDB labels.