↑

Properties

Label 42350.l
Number of curves $2$
Conductor $42350$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 42350.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42350.l1 42350k2 \([1, 1, 0, -1514075, 832914625]\) \(-22187592025/4509428\) \(-78014909932695312500\) \([]\) \(1440000\) \(2.5394\)  
42350.l2 42350k1 \([1, 1, 0, -6415, -4412635]\) \(-659361145/189314048\) \(-8384534604723200\) \([]\) \(288000\) \(1.7346\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 42350.l have rank \(0\).

Complex multiplication

The elliptic curves in class 42350.l do not have complex multiplication.

Modular form 42350.2.a.l

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.