Properties

Label 1792.f
Number of curves $2$
Conductor $1792$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1792.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1792.f1 1792e2 \([0, -1, 0, -29, 5]\) \(85184/49\) \(1605632\) \([2]\) \(256\) \(-0.11964\)  
1792.f2 1792e1 \([0, -1, 0, -19, 39]\) \(1560896/7\) \(3584\) \([2]\) \(128\) \(-0.46622\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1792.f have rank \(0\).

Complex multiplication

The elliptic curves in class 1792.f do not have complex multiplication.

Modular form 1792.2.a.f

sage: E.q_eigenform(10)
 
\(q + 2q^{3} - 2q^{5} - q^{7} + q^{9} + 2q^{13} - 4q^{15} + 6q^{17} + 6q^{19} + O(q^{20})\)  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.