Properties

Label 30960cd
Number of curves $4$
Conductor $30960$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 30960cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.bc3 30960cd1 \([0, 0, 0, -9867, -376774]\) \(35578826569/51600\) \(154076774400\) \([2]\) \(36864\) \(1.0488\) \(\Gamma_0(N)\)-optimal
30960.bc2 30960cd2 \([0, 0, 0, -12747, -138886]\) \(76711450249/41602500\) \(124224399360000\) \([2, 2]\) \(73728\) \(1.3954\)  
30960.bc4 30960cd3 \([0, 0, 0, 49173, -1092454]\) \(4403686064471/2721093750\) \(-8125142400000000\) \([2]\) \(147456\) \(1.7419\)  
30960.bc1 30960cd4 \([0, 0, 0, -120747, 16039514]\) \(65202655558249/512820150\) \(1531272762777600\) \([4]\) \(147456\) \(1.7419\)  

Rank

sage: E.rank()
 

The elliptic curves in class 30960cd have rank \(1\).

Complex multiplication

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

Modular form 30960.2.a.cd

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