Properties

Label 96330di
Number of curves $4$
Conductor $96330$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("di1")
 
E.isogeny_class()
 

Elliptic curves in class 96330di

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96330.de4 96330di1 \([1, 0, 0, 621325, -1131315615]\) \(5495662324535111/117739817533440\) \(-568307610928765992960\) \([2]\) \(5160960\) \(2.6627\) \(\Gamma_0(N)\)-optimal
96330.de3 96330di2 \([1, 0, 0, -13223155, -17531486623]\) \(52974743974734147769/3152005008998400\) \(15214126145478558105600\) \([2, 2]\) \(10321920\) \(3.0093\)  
96330.de2 96330di3 \([1, 0, 0, -39506035, 73791008225]\) \(1412712966892699019449/330160465517040000\) \(1593621506401838325360000\) \([2]\) \(20643840\) \(3.3559\)  
96330.de1 96330di4 \([1, 0, 0, -208451955, -1158409548063]\) \(207530301091125281552569/805586668007040\) \(3888412979416392735360\) \([2]\) \(20643840\) \(3.3559\)  

Rank

sage: E.rank()
 

The elliptic curves in class 96330di have rank \(1\).

Complex multiplication

The elliptic curves in class 96330di do not have complex multiplication.

Modular form 96330.2.a.di

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 4 q^{7} + q^{8} + q^{9} + q^{10} + q^{12} - 4 q^{14} + q^{15} + q^{16} - 2 q^{17} + q^{18} + q^{19} + O(q^{20})\) 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 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.