Properties

Label 270802.f
Number of curves $4$
Conductor $270802$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 270802.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.f1 270802f3 \([1, -1, 0, -9717097916, 368685318380672]\) \(170586815436843383543017473/2166416\) \(1288634759787536\) \([2]\) \(129024000\) \(3.8859\)  
270802.f2 270802f4 \([1, -1, 0, -608866076, 5729990140704]\) \(41966336340198080824833/442001722607124848\) \(262912932528890780348980208\) \([2]\) \(129024000\) \(3.8859\)  
270802.f3 270802f2 \([1, -1, 0, -607318636, 5760821644752]\) \(41647175116728660507393/4693358285056\) \(2791718961759874590976\) \([2, 2]\) \(64512000\) \(3.5393\)  
270802.f4 270802f1 \([1, -1, 0, -37860716, 90501352144]\) \(-10090256344188054273/107965577101312\) \(-64220443125083957297152\) \([2]\) \(32256000\) \(3.1927\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 270802.f have rank \(0\).

Complex multiplication

The elliptic curves in class 270802.f do not have complex multiplication.

Modular form 270802.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2q^{5} - q^{7} - q^{8} - 3q^{9} - 2q^{10} - 4q^{11} + 6q^{13} + q^{14} + q^{16} - 6q^{17} + 3q^{18} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.