Properties

Label 397800.cg
Number of curves $2$
Conductor $397800$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 397800.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
397800.cg1 397800cg1 \([0, 0, 0, -63228675, -193227039250]\) \(2396726313900986596/4154072495625\) \(48453101588970000000000\) \([2]\) \(35389440\) \(3.2468\) \(\Gamma_0(N)\)-optimal
397800.cg2 397800cg2 \([0, 0, 0, -43455675, -316274418250]\) \(-389032340685029858/1627263833203125\) \(-37960810700962500000000000\) \([2]\) \(70778880\) \(3.5934\)  

Rank

sage: E.rank()
 

The elliptic curves in class 397800.cg have rank \(0\).

Complex multiplication

The elliptic curves in class 397800.cg do not have complex multiplication.

Modular form 397800.2.a.cg

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