Properties

Label 363090.dt
Number of curves $4$
Conductor $363090$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dt1")
 
E.isogeny_class()
 

Elliptic curves in class 363090.dt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
363090.dt1 363090dt4 \([1, 0, 1, -5317898, -4720434652]\) \(141369383441705190409/6345626621880\) \(746556626437560120\) \([2]\) \(11796480\) \(2.5063\)  
363090.dt2 363090dt3 \([1, 0, 1, -1652698, 756855908]\) \(4243415895694547209/351514682293320\) \(41355350857126804680\) \([2]\) \(11796480\) \(2.5063\)  
363090.dt3 363090dt2 \([1, 0, 1, -349298, -65850172]\) \(40061018056412809/7275103617600\) \(855908665507022400\) \([2, 2]\) \(5898240\) \(2.1597\)  
363090.dt4 363090dt1 \([1, 0, 1, 42702, -5952572]\) \(73197245859191/172623360000\) \(-20308965680640000\) \([2]\) \(2949120\) \(1.8131\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 363090.dt have rank \(1\).

Complex multiplication

The elliptic curves in class 363090.dt do not have complex multiplication.

Modular form 363090.2.a.dt

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} + q^{12} - q^{13} + q^{15} + q^{16} + 2 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.