Properties

Label 270400.jr
Number of curves $4$
Conductor $270400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("jr1")
 
E.isogeny_class()
 

Elliptic curves in class 270400.jr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270400.jr1 270400jr3 \([0, -1, 0, -56113633, 155314219137]\) \(988345570681/44994560\) \(889569882763427840000000\) \([2]\) \(55738368\) \(3.3574\)  
270400.jr2 270400jr1 \([0, -1, 0, -8793633, -9974540863]\) \(3803721481/26000\) \(514035851264000000000\) \([2]\) \(18579456\) \(2.8081\) \(\Gamma_0(N)\)-optimal
270400.jr3 270400jr2 \([0, -1, 0, -3385633, -22115500863]\) \(-217081801/10562500\) \(-208827064576000000000000\) \([2]\) \(37158912\) \(3.1546\)  
270400.jr4 270400jr4 \([0, -1, 0, 30414367, 590982699137]\) \(157376536199/7722894400\) \(-152686330658691481600000000\) \([2]\) \(111476736\) \(3.7039\)  

Rank

sage: E.rank()
 

The elliptic curves in class 270400.jr have rank \(0\).

Complex multiplication

The elliptic curves in class 270400.jr do not have complex multiplication.

Modular form 270400.2.a.jr

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.