Properties

Label 148120.z
Number of curves $4$
Conductor $148120$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 148120.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
148120.z1 148120m4 \([0, 0, 0, -1821347, -946081586]\) \(4407931365156/100625\) \(15253618002560000\) \([2]\) \(1351680\) \(2.2188\)  
148120.z2 148120m3 \([0, 0, 0, -488267, 117508886]\) \(84923690436/9794435\) \(1484726161897180160\) \([2]\) \(1351680\) \(2.2188\)  
148120.z3 148120m2 \([0, 0, 0, -117967, -13651374]\) \(4790692944/648025\) \(24558324984121600\) \([2, 2]\) \(675840\) \(1.8722\)  
148120.z4 148120m1 \([0, 0, 0, 11638, -1131531]\) \(73598976/276115\) \(-653998871859760\) \([4]\) \(337920\) \(1.5257\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 148120.z have rank \(1\).

Complex multiplication

The elliptic curves in class 148120.z do not have complex multiplication.

Modular form 148120.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{5} + q^{7} - 3 q^{9} + 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.