Properties

Label 139230.m
Number of curves $2$
Conductor $139230$
CM no
Rank $0$
Graph

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

Elliptic curves in class 139230.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139230.m1 139230dl2 \([1, -1, 0, -1629967680, 15279462590976]\) \(656951279855452335833136583681/241839679711912280107200000\) \(176301126509984052198148800000\) \([2]\) \(162570240\) \(4.3120\)  
139230.m2 139230dl1 \([1, -1, 0, 314032320, 1692068990976]\) \(4698067216568883444047416319/4415596696143360000000000\) \(-3218969991488509440000000000\) \([2]\) \(81285120\) \(3.9654\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 139230.m have rank \(0\).

Complex multiplication

The elliptic curves in class 139230.m do not have complex multiplication.

Modular form 139230.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} - 2 q^{11} - q^{13} - q^{14} + q^{16} + q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.