Properties

Label 34848.bv
Number of curves $4$
Conductor $34848$
CM \(\Q(\sqrt{-1}) \)
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bv1")
 
E.isogeny_class()
 

Elliptic curves in class 34848.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
34848.bv1 34848ca3 \([0, 0, 0, -11979, -503118]\) \(287496\) \(661231600128\) \([2]\) \(46080\) \(1.1309\)   \(-16\)
34848.bv2 34848ca4 \([0, 0, 0, -11979, 503118]\) \(287496\) \(661231600128\) \([2]\) \(46080\) \(1.1309\)   \(-16\)
34848.bv3 34848ca1 \([0, 0, 0, -1089, 0]\) \(1728\) \(82653950016\) \([2, 2]\) \(23040\) \(0.78429\) \(\Gamma_0(N)\)-optimal \(-4\)
34848.bv4 34848ca2 \([0, 0, 0, 4356, 0]\) \(1728\) \(-5289852801024\) \([2]\) \(46080\) \(1.1309\)   \(-4\)

Rank

sage: E.rank()
 

The elliptic curves in class 34848.bv have rank \(0\).

Complex multiplication

Each elliptic curve in class 34848.bv has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 34848.2.a.bv

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.