Properties

Label 38646c
Number of curves $2$
Conductor $38646$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 38646c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38646.g2 38646c1 \([1, -1, 0, -923226, -336396556]\) \(4421369023022205171/71573878342336\) \(1408788647412199488\) \([2]\) \(663552\) \(2.2820\) \(\Gamma_0(N)\)-optimal
38646.g1 38646c2 \([1, -1, 0, -14713746, -21719976868]\) \(17897905066884975025011/4805830835912\) \(94593168343255896\) \([2]\) \(1327104\) \(2.6285\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38646c have rank \(0\).

Complex multiplication

The elliptic curves in class 38646c do not have complex multiplication.

Modular form 38646.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2 q^{5} - q^{8} - 2 q^{10} + 2 q^{11} + 4 q^{13} + q^{16} + 4 q^{17} - q^{19} + O(q^{20})\) 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.