Properties

Label 30960.z
Number of curves $4$
Conductor $30960$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.z1 30960s4 \([0, 0, 0, -5323563, -4471229862]\) \(206956783279200843/12642726098000\) \(1019276401815281664000\) \([2]\) \(1327104\) \(2.7832\)  
30960.z2 30960s2 \([0, 0, 0, -5242923, -4620705958]\) \(144118734029937784467/37867520\) \(4187844771840\) \([2]\) \(442368\) \(2.2339\)  
30960.z3 30960s3 \([0, 0, 0, -1003563, 300642138]\) \(1386456968640843/318028000000\) \(25639916027904000000\) \([2]\) \(663552\) \(2.4366\)  
30960.z4 30960s1 \([0, 0, 0, -327723, -72179878]\) \(35198225176082067/18035507200\) \(1994582812262400\) \([2]\) \(221184\) \(1.8873\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 30960.z have rank \(0\).

Complex multiplication

The elliptic curves in class 30960.z do not have complex multiplication.

Modular form 30960.2.a.z

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

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.