Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1792.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1792.g1 1792c2 \([0, -1, 0, -77, -235]\) \(1560896/7\) \(229376\) \([2]\) \(256\) \(-0.11964\)  
1792.g2 1792c1 \([0, -1, 0, -7, 3]\) \(85184/49\) \(25088\) \([2]\) \(128\) \(-0.46622\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1792.2.a.g

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.