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Properties

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

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 3150.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3150.m1 3150u2 \([1, -1, 0, -10242, 563166]\) \(-417267265/235298\) \(-67004782031250\) \([3]\) \(10800\) \(1.3562\)  
3150.m2 3150u1 \([1, -1, 0, 1008, -10584]\) \(397535/392\) \(-111628125000\) \([]\) \(3600\) \(0.80685\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3150.2.a.m

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.