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Properties

Label 308550.u
Number of curves $2$
Conductor $308550$
CM no
Rank $1$
Graph

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

Elliptic curves in class 308550.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308550.u1 308550u2 \([1, 1, 0, -35097625, 80017553125]\) \(172735174415217961/39657600\) \(1097747773650000000\) \([2]\) \(20643840\) \(2.8423\)  
308550.u2 308550u1 \([1, 1, 0, -2185625, 1259137125]\) \(-41713327443241/639221760\) \(-17694067818240000000\) \([2]\) \(10321920\) \(2.4958\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 308550.u have rank \(1\).

Complex multiplication

The elliptic curves in class 308550.u do not have complex multiplication.

Modular form 308550.2.a.u

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