Properties

Label 297024.r
Number of curves $4$
Conductor $297024$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 297024.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
297024.r1 297024r4 \([0, -1, 0, -20783363329, -1153238810620031]\) \(15149254835477430732977727429892/243555039\) \(15961623035904\) \([2]\) \(171442176\) \(4.0080\)  
297024.r2 297024r2 \([0, -1, 0, -1298960209, -18019031639471]\) \(14794194217980649552803358288/59319057022291521\) \(971883430253224280064\) \([2, 2]\) \(85721088\) \(3.6614\)  
297024.r3 297024r3 \([0, -1, 0, -1298335969, -18037216125215]\) \(-3693218893320489942273647332/7406340191177313578283\) \(-485381910768996422666354688\) \([2]\) \(171442176\) \(4.0080\)  
297024.r4 297024r1 \([0, -1, 0, -81224029, -281242894355]\) \(57873179869926460658341888/115712943163950039453\) \(118490053799884840399872\) \([2]\) \(42860544\) \(3.3148\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 297024.r have rank \(0\).

Complex multiplication

The elliptic curves in class 297024.r do not have complex multiplication.

Modular form 297024.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} - q^{7} + q^{9} - q^{13} + 2 q^{15} + q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.