Properties

Label 42350.co
Number of curves $2$
Conductor $42350$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("co1")
 
E.isogeny_class()
 

Elliptic curves in class 42350.co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42350.co1 42350db1 \([1, -1, 1, -1178805, 492790697]\) \(52355598021/15092\) \(52219528539062500\) \([2]\) \(691200\) \(2.1879\) \(\Gamma_0(N)\)-optimal
42350.co2 42350db2 \([1, -1, 1, -1027555, 623773197]\) \(-34677868581/28471058\) \(-98512140588941406250\) \([2]\) \(1382400\) \(2.5344\)  

Rank

sage: E.rank()
 

The elliptic curves in class 42350.co have rank \(1\).

Complex multiplication

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

Modular form 42350.2.a.co

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} - 3 q^{9} + 6 q^{13} + q^{14} + q^{16} + 4 q^{17} - 3 q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.