Properties

Label 3150.a
Number of curves $2$
Conductor $3150$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3150.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.a1 3150m2 \([1, -1, 0, -78867, 9039541]\) \(-7620530425/526848\) \(-3750705000000000\) \([]\) \(25920\) \(1.7393\)  
3150.a2 3150m1 \([1, -1, 0, 5508, 11416]\) \(2595575/1512\) \(-10764140625000\) \([]\) \(8640\) \(1.1900\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3150.a have rank \(0\).

Complex multiplication

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

Modular form 3150.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} - 6q^{11} + q^{13} + q^{14} + q^{16} + 3q^{17} - 4q^{19} + O(q^{20})\)  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.