Properties

Label 93600.k
Number of curves $4$
Conductor $93600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 93600.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.k1 93600dp4 \([0, 0, 0, -51192075, 140934735250]\) \(2543984126301795848/909361981125\) \(5303399073921000000000\) \([2]\) \(9437184\) \(3.1378\)  
93600.k2 93600dp3 \([0, 0, 0, -26442075, -51258577250]\) \(350584567631475848/8259273550125\) \(48168083344329000000000\) \([2]\) \(9437184\) \(3.1378\)  
93600.k3 93600dp1 \([0, 0, 0, -3660825, 1525579000]\) \(7442744143086784/2927948765625\) \(2134474650140625000000\) \([2, 2]\) \(4718592\) \(2.7912\) \(\Gamma_0(N)\)-optimal
93600.k4 93600dp2 \([0, 0, 0, 11739300, 11012056000]\) \(3834800837445824/3342041015625\) \(-155926265625000000000000\) \([2]\) \(9437184\) \(3.1378\)  

Rank

sage: E.rank()
 

The elliptic curves in class 93600.k have rank \(1\).

Complex multiplication

The elliptic curves in class 93600.k do not have complex multiplication.

Modular form 93600.2.a.k

sage: E.q_eigenform(10)
 
\(q - 4q^{7} - q^{13} + 2q^{17} + 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.