Properties

Label 308550ec
Number of curves $4$
Conductor $308550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ec1")
 
E.isogeny_class()
 

Elliptic curves in class 308550ec

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308550.ec4 308550ec1 \([1, 0, 1, -10731251, 2218704398]\) \(4937402992298041/2780405760000\) \(76963412634240000000000\) \([2]\) \(26542080\) \(3.0816\) \(\Gamma_0(N)\)-optimal
308550.ec2 308550ec2 \([1, 0, 1, -107531251, -426992495602]\) \(4967657717692586041/29490113030400\) \(816305220785132100000000\) \([2, 2]\) \(53084160\) \(3.4281\)  
308550.ec3 308550ec3 \([1, 0, 1, -45821251, -913637555602]\) \(-384369029857072441/12804787777021680\) \(-354444728735129756913750000\) \([2]\) \(106168320\) \(3.7747\)  
308550.ec1 308550ec4 \([1, 0, 1, -1718041251, -27409477035602]\) \(20260414982443110947641/720358602480\) \(19939987596376113750000\) \([2]\) \(106168320\) \(3.7747\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 308550.2.a.ec

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