↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 3150.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.h1 3150a1 \([1, -1, 0, -57, 181]\) \(-30642435/56\) \(-37800\) \([]\) \(288\) \(-0.23008\) \(\Gamma_0(N)\)-optimal
3150.h2 3150a2 \([1, -1, 0, 93, 791]\) \(179685/686\) \(-337563450\) \([]\) \(864\) \(0.31923\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3150.2.a.h

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.