Properties

Label 94864.db
Number of curves $2$
Conductor $94864$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("db1")
 
E.isogeny_class()
 

Elliptic curves in class 94864.db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
94864.db1 94864cs2 \([0, -1, 0, -4887472, -3837475200]\) \(15124197817/1294139\) \(1104803965116409327616\) \([2]\) \(4423680\) \(2.7790\)  
94864.db2 94864cs1 \([0, -1, 0, 330048, -277039552]\) \(4657463/41503\) \(-35431030951255109632\) \([2]\) \(2211840\) \(2.4325\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 94864.db have rank \(0\).

Complex multiplication

The elliptic curves in class 94864.db do not have complex multiplication.

Modular form 94864.2.a.db

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.