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Properties

Label 139425.m
Number of curves $2$
Conductor $139425$
CM no
Rank $0$
Graph

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

Elliptic curves in class 139425.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139425.m1 139425g2 \([1, 0, 0, -55013, 3731142]\) \(244140625/61347\) \(4626722683171875\) \([2]\) \(774144\) \(1.7158\)  
139425.m2 139425g1 \([1, 0, 0, 8362, 372267]\) \(857375/1287\) \(-97064112234375\) \([2]\) \(387072\) \(1.3693\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 139425.m have rank \(0\).

Complex multiplication

The elliptic curves in class 139425.m do not have complex multiplication.

Modular form 139425.2.a.m

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.