Properties

Label 1152.m
Number of curves $2$
Conductor $1152$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1152.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.m1 1152s2 \([0, 0, 0, -84, -272]\) \(10976\) \(5971968\) \([2]\) \(192\) \(0.039450\)  
1152.m2 1152s1 \([0, 0, 0, 6, -20]\) \(128\) \(-186624\) \([2]\) \(96\) \(-0.30712\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1152.m have rank \(1\).

Complex multiplication

The elliptic curves in class 1152.m do not have complex multiplication.

Modular form 1152.2.a.m

sage: E.q_eigenform(10)
 
\(q + 2q^{5} - 4q^{7} - 2q^{11} - 2q^{13} + 2q^{17} - 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.