Properties

Label 60984bh
Number of curves $4$
Conductor $60984$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 60984bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.s3 60984bh1 \([0, 0, 0, -7986, -272855]\) \(2725888/21\) \(433933237584\) \([2]\) \(92160\) \(1.0621\) \(\Gamma_0(N)\)-optimal
60984.s2 60984bh2 \([0, 0, 0, -13431, 146410]\) \(810448/441\) \(145801567828224\) \([2, 2]\) \(184320\) \(1.4086\)  
60984.s4 60984bh3 \([0, 0, 0, 51909, 1152646]\) \(11696828/7203\) \(-9525702431443968\) \([2]\) \(368640\) \(1.7552\)  
60984.s1 60984bh4 \([0, 0, 0, -165891, 25973134]\) \(381775972/567\) \(749836634545152\) \([2]\) \(368640\) \(1.7552\)  

Rank

sage: E.rank()
 

The elliptic curves in class 60984bh have rank \(0\).

Complex multiplication

The elliptic curves in class 60984bh do not have complex multiplication.

Modular form 60984.2.a.bh

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + q^{7} + 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.