Properties

Label 3042.n
Number of curves $4$
Conductor $3042$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3042.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3042.n1 3042n4 \([1, -1, 1, -638969, -196432999]\) \(18013780041269221/9216\) \(14760465408\) \([2]\) \(19200\) \(1.7193\)  
3042.n2 3042n3 \([1, -1, 1, -39929, -3062887]\) \(-4395631034341/3145728\) \(-5038238859264\) \([2]\) \(9600\) \(1.3727\)  
3042.n3 3042n2 \([1, -1, 1, -1904, 12575]\) \(476379541/236196\) \(378294584148\) \([2]\) \(3840\) \(0.91459\)  
3042.n4 3042n1 \([1, -1, 1, 436, 1343]\) \(5735339/3888\) \(-6227071344\) \([2]\) \(1920\) \(0.56802\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3042.n have rank \(0\).

Complex multiplication

The elliptic curves in class 3042.n do not have complex multiplication.

Modular form 3042.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 2 q^{5} - 2 q^{7} + q^{8} + 2 q^{10} - 2 q^{14} + q^{16} - 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.