Properties

Label 463680.ip
Number of curves $2$
Conductor $463680$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ip1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 463680.ip

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.ip1 463680ip1 \([0, 0, 0, -2837722572, -24326957092464]\) \(489781415227546051766883/233890092903563264000\) \(1206821505891260360376188928000\) \([2]\) \(594542592\) \(4.4660\) \(\Gamma_0(N)\)-optimal
463680.ip2 463680ip2 \([0, 0, 0, 10185591348, -185029441539696]\) \(22649115256119592694355357/15973509811739648000000\) \(-82419802079093454689796096000000\) \([2]\) \(1189085184\) \(4.8126\)  

Rank

sage: E.rank()
 

The elliptic curves in class 463680.ip have rank \(0\).

Complex multiplication

The elliptic curves in class 463680.ip do not have complex multiplication.

Modular form 463680.2.a.ip

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