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Properties

Label 274890dt
Number of curves $2$
Conductor $274890$
CM no
Rank $1$
Graph

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

Elliptic curves in class 274890dt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
274890.dt2 274890dt1 \([1, 1, 1, -43121, -1535857]\) \(75370704203521/35157196800\) \(4136209046323200\) \([2]\) \(1935360\) \(1.6910\) \(\Gamma_0(N)\)-optimal
274890.dt1 274890dt2 \([1, 1, 1, -576241, -168509041]\) \(179865548102096641/119964240000\) \(14113672871760000\) \([2]\) \(3870720\) \(2.0376\)  

Rank

sage: E.rank()
 

The elliptic curves in class 274890dt have rank \(1\).

Complex multiplication

The elliptic curves in class 274890dt do not have complex multiplication.

Modular form 274890.2.a.dt

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} - q^{11} - q^{12} + 4 q^{13} + q^{15} + q^{16} - q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.