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Properties

Label 270802m
Number of curves $2$
Conductor $270802$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 270802m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.m2 270802m1 \([1, 0, 0, -9085627039, 335121441237705]\) \(-139444195316122186685933977/867810592237096964848\) \(-516193978473446836029907620208\) \([2]\) \(611143680\) \(4.5396\) \(\Gamma_0(N)\)-optimal
270802.m1 270802m2 \([1, 0, 0, -145586470019, 21381067113411469]\) \(573718392227901342193352375257/22016176259779893044\) \(13095735078563634709456879124\) \([2]\) \(1222287360\) \(4.8862\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270802m have rank \(1\).

Complex multiplication

The elliptic curves in class 270802m do not have complex multiplication.

Modular form 270802.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + q^{8} + q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} + 2 q^{13} + q^{14} + 4 q^{15} + q^{16} + q^{18} - 2 q^{19} + O(q^{20})\) 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.