Properties

Label 1152.t
Number of curves $2$
Conductor $1152$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1152.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.t1 1152i1 \([0, 0, 0, -318, 2180]\) \(19056256/27\) \(5038848\) \([2]\) \(384\) \(0.18920\) \(\Gamma_0(N)\)-optimal
1152.t2 1152i2 \([0, 0, 0, -228, 3440]\) \(-219488/729\) \(-4353564672\) \([2]\) \(768\) \(0.53578\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1152.t have rank \(0\).

Complex multiplication

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

Modular form 1152.2.a.t

sage: E.q_eigenform(10)
 
\(q + 4q^{5} + 2q^{7} - 4q^{11} + 2q^{13} + 2q^{17} + 8q^{19} + O(q^{20})\)  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.