↑

Properties

Label 43350r
Number of curves $2$
Conductor $43350$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 43350r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43350.r2 43350r1 \([1, 1, 0, -2080950, 1154416500]\) \(105695235625/14688\) \(138489302137500000\) \([]\) \(1036800\) \(2.3063\) \(\Gamma_0(N)\)-optimal
43350.r1 43350r2 \([1, 1, 0, -4790325, -2398657875]\) \(1289333385625/482967552\) \(4553774457484800000000\) \([]\) \(3110400\) \(2.8556\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43350r have rank \(0\).

Complex multiplication

The elliptic curves in class 43350r do not have complex multiplication.

Modular form 43350.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} + 3 q^{11} - q^{12} + 2 q^{13} - q^{14} + q^{16} - q^{18} - 7 q^{19} + O(q^{20})\) 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 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.