Properties

Label 303450.t
Number of curves $6$
Conductor $303450$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 303450.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.t1 303450t3 \([1, 1, 0, -9710550, 11642949000]\) \(268498407453697/252\) \(95041677937500\) \([2]\) \(10485760\) \(2.4104\)  
303450.t2 303450t6 \([1, 1, 0, -6603800, -6471932250]\) \(84448510979617/933897762\) \(352219088581571531250\) \([2]\) \(20971520\) \(2.7570\)  
303450.t3 303450t4 \([1, 1, 0, -751550, 88440000]\) \(124475734657/63011844\) \(23764886443238062500\) \([2, 2]\) \(10485760\) \(2.4104\)  
303450.t4 303450t2 \([1, 1, 0, -607050, 181642500]\) \(65597103937/63504\) \(23950502840250000\) \([2, 2]\) \(5242880\) \(2.0639\)  
303450.t5 303450t1 \([1, 1, 0, -29050, 4196500]\) \(-7189057/16128\) \(-6082667388000000\) \([2]\) \(2621440\) \(1.7173\) \(\Gamma_0(N)\)-optimal
303450.t6 303450t5 \([1, 1, 0, 2788700, 686742250]\) \(6359387729183/4218578658\) \(-1591034897490662531250\) \([2]\) \(20971520\) \(2.7570\)  

Rank

sage: E.rank()
 

The elliptic curves in class 303450.t have rank \(1\).

Complex multiplication

The elliptic curves in class 303450.t do not have complex multiplication.

Modular form 303450.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 4q^{11} - q^{12} - 6q^{13} + q^{14} + q^{16} - q^{18} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.