Properties

Label 30960.c
Number of curves $2$
Conductor $30960$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30960.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
30960.c1 30960w2 \([0, 0, 0, -20000043, 34426629658]\) \(8000051600110940079507/144453125\) \(15975360000000\) \([2]\) \(1146880\) \(2.5244\)  
30960.c2 30960w1 \([0, 0, 0, -1250043, 537879658]\) \(1953326569433829507/262451171875\) \(29025000000000000\) \([2]\) \(573440\) \(2.1778\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 30960.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4q^{7} + 4q^{11} + 2q^{13} - 6q^{17} + 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.