Properties

Label 7800.u
Number of curves $4$
Conductor $7800$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7800.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7800.u1 7800t4 \([0, 1, 0, -145408, 21286688]\) \(10625310339698/3855735\) \(123383520000000\) \([2]\) \(36864\) \(1.6724\)  
7800.u2 7800t3 \([0, 1, 0, -75408, -7833312]\) \(1481943889298/34543665\) \(1105397280000000\) \([2]\) \(36864\) \(1.6724\)  
7800.u3 7800t2 \([0, 1, 0, -10408, 226688]\) \(7793764996/3080025\) \(49280400000000\) \([2, 2]\) \(18432\) \(1.3258\)  
7800.u4 7800t1 \([0, 1, 0, 2092, 26688]\) \(253012016/219375\) \(-877500000000\) \([2]\) \(9216\) \(0.97923\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7800.u have rank \(1\).

Complex multiplication

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

Modular form 7800.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} + 4 q^{11} - q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\)  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.