Show commands:
SageMath
E = EllipticCurve("ik1")
E.isogeny_class()
Elliptic curves in class 224400.ik
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.ik1 | 224400cx3 | \([0, 1, 0, -561698808, 5123744882388]\) | \(306234591284035366263793/1727485056\) | \(110559043584000000\) | \([2]\) | \(33030144\) | \(3.3401\) | |
| 224400.ik2 | 224400cx2 | \([0, 1, 0, -35106808, 80046706388]\) | \(74768347616680342513/5615307472896\) | \(359379678265344000000\) | \([2, 2]\) | \(16515072\) | \(2.9936\) | |
| 224400.ik3 | 224400cx4 | \([0, 1, 0, -32802808, 91009138388]\) | \(-60992553706117024753/20624795251201152\) | \(-1319986896076873728000000\) | \([2]\) | \(33030144\) | \(3.3401\) | |
| 224400.ik4 | 224400cx1 | \([0, 1, 0, -2338808, 1075826388]\) | \(22106889268753393/4969545596928\) | \(318050918203392000000\) | \([2]\) | \(8257536\) | \(2.6470\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 224400.ik have rank \(0\).
Complex multiplication
The elliptic curves in class 224400.ik do not have complex multiplication.Modular form 224400.2.a.ik
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
