Properties

Label 124128.i
Number of curves $2$
Conductor $124128$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 124128.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124128.i1 124128b2 \([0, 0, 0, -15660, -730944]\) \(5268024000/185761\) \(14976343093248\) \([2]\) \(199680\) \(1.2990\)  
124128.i2 124128b1 \([0, 0, 0, -15525, -744552]\) \(328509000000/431\) \(542935872\) \([2]\) \(99840\) \(0.95238\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 124128.i have rank \(0\).

Complex multiplication

The elliptic curves in class 124128.i do not have complex multiplication.

Modular form 124128.2.a.i

sage: E.q_eigenform(10)
 
\(q + 2 q^{7} - 4 q^{11} - 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.