Properties

Label 3150.n
Number of curves $2$
Conductor $3150$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 3150.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.n1 3150n2 \([1, -1, 0, -984492, 376227666]\) \(-14822892630025/42\) \(-299003906250\) \([]\) \(24000\) \(1.8586\)  
3150.n2 3150n1 \([1, -1, 0, 198, 74196]\) \(46969655/130691232\) \(-2381847703200\) \([]\) \(4800\) \(1.0539\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3150.n have rank \(1\).

Complex multiplication

The elliptic curves in class 3150.n do not have complex multiplication.

Modular form 3150.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - 2 q^{11} - q^{13} - q^{14} + q^{16} - 3 q^{17} + O(q^{20})\) 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.