Properties

Label 194810.c
Number of curves $4$
Conductor $194810$
CM no
Rank $1$
Graph

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

Elliptic curves in class 194810.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
194810.c1 194810p4 \([1, 0, 1, -20186554, 34907522802]\) \(513516182162686336369/1944885031250\) \(3445482470846281250\) \([2]\) \(16174080\) \(2.7716\)  
194810.c2 194810p3 \([1, 0, 1, -1280304, 528397802]\) \(131010595463836369/7704101562500\) \(13648285868164062500\) \([2]\) \(8087040\) \(2.4250\)  
194810.c3 194810p2 \([1, 0, 1, -343764, 8279786]\) \(2535986675931409/1450751712200\) \(2570095154016744200\) \([2]\) \(5391360\) \(2.2223\)  
194810.c4 194810p1 \([1, 0, 1, -222764, -40313814]\) \(690080604747409/3406760000\) \(6035283152360000\) \([2]\) \(2695680\) \(1.8757\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 194810.c have rank \(1\).

Complex multiplication

The elliptic curves in class 194810.c do not have complex multiplication.

Modular form 194810.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} - q^{5} + 2 q^{6} - q^{7} - q^{8} + q^{9} + q^{10} - 2 q^{12} + 4 q^{13} + q^{14} + 2 q^{15} + q^{16} - 6 q^{17} - q^{18} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.