Properties

Label 436800.c
Number of curves $2$
Conductor $436800$
CM no
Rank $1$
Graph

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

Elliptic curves in class 436800.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436800.c1 436800c1 \([0, -1, 0, -13778833, 19686535537]\) \(9040887701683472/2380530789\) \(76176985248000000000\) \([2]\) \(29491200\) \(2.7995\) \(\Gamma_0(N)\)-optimal
436800.c2 436800c2 \([0, -1, 0, -12088833, 24694005537]\) \(-1526394922573748/1174052430369\) \(-150278711087232000000000\) \([2]\) \(58982400\) \(3.1461\)  

Rank

sage: E.rank()
 

The elliptic curves in class 436800.c have rank \(1\).

Complex multiplication

The elliptic curves in class 436800.c do not have complex multiplication.

Modular form 436800.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.