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SageMath
E = EllipticCurve("hk1")
E.isogeny_class()
Elliptic curves in class 203280hk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.r2 | 203280hk1 | \([0, -1, 0, -159276, -16612704]\) | \(740292464/229635\) | \(138615633413832960\) | \([2]\) | \(1892352\) | \(1.9937\) | \(\Gamma_0(N)\)-optimal |
| 203280.r1 | 203280hk2 | \([0, -1, 0, -2315496, -1355194080]\) | \(568619673836/99225\) | \(239582576270822400\) | \([2]\) | \(3784704\) | \(2.3402\) |
Rank
sage: E.rank()
The elliptic curves in class 203280hk have rank \(1\).
Complex multiplication
The elliptic curves in class 203280hk do not have complex multiplication.Modular form 203280.2.a.hk
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 Cremona 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 Cremona labels.
