Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3150.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.x1 3150bh2 \([1, -1, 1, -410, 4587]\) \(-417267265/235298\) \(-4288306050\) \([]\) \(2160\) \(0.55144\)  
3150.x2 3150bh1 \([1, -1, 1, 40, -93]\) \(397535/392\) \(-7144200\) \([]\) \(720\) \(0.0021345\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3150.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} - 3 q^{11} - 2 q^{13} - q^{14} + q^{16} + 3 q^{17} - 7 q^{19} + O(q^{20})\)  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.