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Properties

Label 3234.m
Number of curves $2$
Conductor $3234$
CM no
Rank $0$
Graph

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

Elliptic curves in class 3234.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3234.m1 3234m2 \([1, 0, 1, -3541011, -2565008834]\) \(121681065322255375/12702096\) \(512575390060272\) \([2]\) \(57344\) \(2.2515\)  
3234.m2 3234m1 \([1, 0, 1, -220771, -40298338]\) \(-29489309167375/303595776\) \(-12251184631564032\) \([2]\) \(28672\) \(1.9049\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3234.m have rank \(0\).

Complex multiplication

The elliptic curves in class 3234.m do not have complex multiplication.

Modular form 3234.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + q^{11} + q^{12} + 4 q^{13} + q^{16} - 4 q^{17} - q^{18} + O(q^{20})\) 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.