Properties

Label 463680.kt
Number of curves $2$
Conductor $463680$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("kt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 463680.kt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.kt1 463680kt1 \([0, 0, 0, -141132, 19481744]\) \(1626794704081/83462400\) \(15949913024102400\) \([2]\) \(4718592\) \(1.8669\) \(\Gamma_0(N)\)-optimal
463680.kt2 463680kt2 \([0, 0, 0, 89268, 76897424]\) \(411664745519/13605414480\) \(-2600035196841492480\) \([2]\) \(9437184\) \(2.2135\)  

Rank

sage: E.rank()
 

The elliptic curves in class 463680.kt have rank \(1\).

Complex multiplication

The elliptic curves in class 463680.kt do not have complex multiplication.

Modular form 463680.2.a.kt

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} + 6q^{11} - 6q^{17} - 8q^{19} + O(q^{20})\)  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.