Properties

Label 82800cs
Number of curves $2$
Conductor $82800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cs1")
 
E.isogeny_class()
 

Elliptic curves in class 82800cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
82800.k2 82800cs1 \([0, 0, 0, -3675, 74250]\) \(3176523/460\) \(794880000000\) \([2]\) \(110592\) \(1.0087\) \(\Gamma_0(N)\)-optimal
82800.k1 82800cs2 \([0, 0, 0, -15675, -681750]\) \(246491883/26450\) \(45705600000000\) \([2]\) \(221184\) \(1.3553\)  

Rank

sage: E.rank()
 

The elliptic curves in class 82800cs have rank \(1\).

Complex multiplication

The elliptic curves in class 82800cs do not have complex multiplication.

Modular form 82800.2.a.cs

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} + 4 q^{17} - 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.