Properties

Label 30096bd
Number of curves $2$
Conductor $30096$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 30096bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30096.o2 30096bd1 \([0, 0, 0, -52320, -4965712]\) \(-5304438784000/497763387\) \(-1486313509367808\) \([]\) \(103680\) \(1.6533\) \(\Gamma_0(N)\)-optimal
30096.o1 30096bd2 \([0, 0, 0, -4329120, -3466949776]\) \(-3004935183806464000/2037123\) \(-6082816684032\) \([]\) \(311040\) \(2.2026\)  

Rank

sage: E.rank()
 

The elliptic curves in class 30096bd have rank \(0\).

Complex multiplication

The elliptic curves in class 30096bd do not have complex multiplication.

Modular form 30096.2.a.bd

sage: E.q_eigenform(10)
 
\(q - 2 q^{7} + q^{11} - q^{13} - 3 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.