Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 3150.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.l1 3150j2 \([1, -1, 0, -162, -754]\) \(139798359/98\) \(330750\) \([2]\) \(768\) \(-0.0045635\)  
3150.l2 3150j1 \([1, -1, 0, -12, -4]\) \(59319/28\) \(94500\) \([2]\) \(384\) \(-0.35114\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3150.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - 6 q^{11} - 2 q^{13} - q^{14} + q^{16} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.