Properties

Label 35280.es
Number of curves $4$
Conductor $35280$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("es1")
 
E.isogeny_class()
 

Elliptic curves in class 35280.es

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35280.es1 35280ff4 \([0, 0, 0, -793947, 272272714]\) \(157551496201/13125\) \(4610786664960000\) \([4]\) \(393216\) \(2.0494\)  
35280.es2 35280ff2 \([0, 0, 0, -53067, 3629626]\) \(47045881/11025\) \(3873060798566400\) \([2, 2]\) \(196608\) \(1.7029\)  
35280.es3 35280ff1 \([0, 0, 0, -17787, -865046]\) \(1771561/105\) \(36886293319680\) \([2]\) \(98304\) \(1.3563\) \(\Gamma_0(N)\)-optimal
35280.es4 35280ff3 \([0, 0, 0, 123333, 22645546]\) \(590589719/972405\) \(-341603962433556480\) \([2]\) \(393216\) \(2.0494\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35280.es have rank \(1\).

Complex multiplication

The elliptic curves in class 35280.es do not have complex multiplication.

Modular form 35280.2.a.es

sage: E.q_eigenform(10)
 
\(q + q^{5} + 6 q^{13} + 2 q^{17} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.