Properties

Label 5070.t
Number of curves $4$
Conductor $5070$
CM no
Rank $1$
Graph

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

Elliptic curves in class 5070.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.t1 5070t4 \([1, 0, 0, -147465601, -689269402615]\) \(73474353581350183614361/576510977802240\) \(2782708376254652252160\) \([2]\) \(725760\) \(3.2879\)  
5070.t2 5070t3 \([1, 0, 0, -9020801, -11249839095]\) \(-16818951115904497561/1592332281446400\) \(-7685883787076016537600\) \([2]\) \(362880\) \(2.9413\)  
5070.t3 5070t2 \([1, 0, 0, -2704426, 64216580]\) \(453198971846635561/261896250564000\) \(1264123179288570276000\) \([2]\) \(241920\) \(2.7386\)  
5070.t4 5070t1 \([1, 0, 0, 675574, 8108580]\) \(7064514799444439/4094064000000\) \(-19761264961776000000\) \([2]\) \(120960\) \(2.3920\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5070.t have rank \(1\).

Complex multiplication

The elliptic curves in class 5070.t do not have complex multiplication.

Modular form 5070.2.a.t

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.