Properties

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

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 308550d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308550.d2 308550d1 \([1, 1, 0, -1420051525, 20580847298125]\) \(8595711443128766579/7520256000000\) \(277068285483264000000000000\) \([2]\) \(273715200\) \(3.9996\) \(\Gamma_0(N)\)-optimal
308550.d1 308550d2 \([1, 1, 0, -22716051525, 1317784095298125]\) \(35185850652034529726579/26967168000\) \(993549554975142000000000\) \([2]\) \(547430400\) \(4.3462\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 308550.2.a.d

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