Properties

Label 72450.p
Number of curves $4$
Conductor $72450$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72450.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.p1 72450u3 \([1, -1, 0, -649692, 66451216]\) \(2662558086295801/1374177967680\) \(15652745913105000000\) \([2]\) \(1658880\) \(2.3752\)  
72450.p2 72450u1 \([1, -1, 0, -362817, -84023159]\) \(463702796512201/15214500\) \(173302664062500\) \([2]\) \(552960\) \(1.8259\) \(\Gamma_0(N)\)-optimal
72450.p3 72450u2 \([1, -1, 0, -347067, -91661909]\) \(-405897921250921/84358968750\) \(-960901378417968750\) \([2]\) \(1105920\) \(2.1724\)  
72450.p4 72450u4 \([1, -1, 0, 2437308, 514066216]\) \(140574743422291079/91397357868600\) \(-1041073029472021875000\) \([2]\) \(3317760\) \(2.7218\)  

Rank

sage: E.rank()
 

The elliptic curves in class 72450.p have rank \(0\).

Complex multiplication

The elliptic curves in class 72450.p do not have complex multiplication.

Modular form 72450.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} - 2q^{13} + q^{14} + q^{16} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.