Properties

Label 3150.t
Number of curves 4
Conductor 3150
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("3150.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3150.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.t1 3150o3 [1, -1, 0, -84042, -9356634] [2] 12288  
3150.t2 3150o2 [1, -1, 0, -5292, -142884] [2, 2] 6144  
3150.t3 3150o1 [1, -1, 0, -792, 5616] [2] 3072 \(\Gamma_0(N)\)-optimal
3150.t4 3150o4 [1, -1, 0, 1458, -487134] [2] 12288  

Rank

sage: E.rank()
 

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

Modular form 3150.2.a.t

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.