Properties

Label 7800.k
Number of curves $4$
Conductor $7800$
CM no
Rank $0$
Graph

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

Elliptic curves in class 7800.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7800.k1 7800m3 \([0, -1, 0, -41408, -3217188]\) \(490757540836/2142075\) \(34273200000000\) \([2]\) \(36864\) \(1.4500\)  
7800.k2 7800m2 \([0, -1, 0, -3908, 7812]\) \(1650587344/950625\) \(3802500000000\) \([2, 2]\) \(18432\) \(1.1035\)  
7800.k3 7800m1 \([0, -1, 0, -2783, 57312]\) \(9538484224/26325\) \(6581250000\) \([2]\) \(9216\) \(0.75689\) \(\Gamma_0(N)\)-optimal
7800.k4 7800m4 \([0, -1, 0, 15592, 46812]\) \(26198797244/15234375\) \(-243750000000000\) \([2]\) \(36864\) \(1.4500\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7800.k have rank \(0\).

Complex multiplication

The elliptic curves in class 7800.k do not have complex multiplication.

Modular form 7800.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.