Properties

Label 141120.mg
Number of curves $4$
Conductor $141120$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("mg1")
 
E.isogeny_class()
 

Elliptic curves in class 141120.mg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.mg1 141120gg3 \([0, 0, 0, -2968812, -1966443696]\) \(4767078987/6860\) \(4164314970618593280\) \([2]\) \(2654208\) \(2.4752\)  
141120.mg2 141120gg4 \([0, 0, 0, -2122092, -3111547824]\) \(-1740992427/5882450\) \(-3570900087305443737600\) \([2]\) \(5308416\) \(2.8218\)  
141120.mg3 141120gg1 \([0, 0, 0, -146412, 18895184]\) \(416832723/56000\) \(46631560937472000\) \([2]\) \(884736\) \(1.9259\) \(\Gamma_0(N)\)-optimal
141120.mg4 141120gg2 \([0, 0, 0, 229908, 100029776]\) \(1613964717/6125000\) \(-5100326977536000000\) \([2]\) \(1769472\) \(2.2725\)  

Rank

sage: E.rank()
 

The elliptic curves in class 141120.mg have rank \(0\).

Complex multiplication

The elliptic curves in class 141120.mg do not have complex multiplication.

Modular form 141120.2.a.mg

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2 q^{13} - 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.