Properties

Label 438.c
Number of curves $4$
Conductor $438$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 438.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
438.c1 438d4 \([1, 0, 1, -32681, 1883180]\) \(3860029467400479625/697348114739712\) \(697348114739712\) \([2]\) \(3456\) \(1.5671\)  
438.c2 438d2 \([1, 0, 1, -31106, 2108972]\) \(3328404840479049625/31078728\) \(31078728\) \([6]\) \(1152\) \(1.0178\)  
438.c3 438d3 \([1, 0, 1, -9641, -337876]\) \(99088945018143625/8260256268288\) \(8260256268288\) \([2]\) \(1728\) \(1.2206\)  
438.c4 438d1 \([1, 0, 1, -1946, 32780]\) \(814388006841625/2482892352\) \(2482892352\) \([6]\) \(576\) \(0.67126\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 438.c have rank \(1\).

Complex multiplication

The elliptic curves in class 438.c do not have complex multiplication.

Modular form 438.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - 4 q^{7} - q^{8} + q^{9} - 6 q^{11} + q^{12} - 4 q^{13} + 4 q^{14} + q^{16} - 6 q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.