Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("3150.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3150.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.p1 3150i2 [1, -1, 0, -511617, 140980541] [2] 30720  
3150.p2 3150i1 [1, -1, 0, -31617, 2260541] [2] 15360 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 3150.2.a.p

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

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.