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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 62832.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62832.bk1 | 62832bz4 | \([0, 1, 0, -1096744, -442451020]\) | \(35618855581745079337/188166132\) | \(770728476672\) | \([2]\) | \(442368\) | \(1.8974\) | |
| 62832.bk2 | 62832bz2 | \([0, 1, 0, -68584, -6922444]\) | \(8710408612492777/19986042384\) | \(81862829604864\) | \([2, 2]\) | \(221184\) | \(1.5508\) | |
| 62832.bk3 | 62832bz3 | \([0, 1, 0, -43944, -11939148]\) | \(-2291249615386537/13671036998388\) | \(-55996567545397248\) | \([2]\) | \(442368\) | \(1.8974\) | |
| 62832.bk4 | 62832bz1 | \([0, 1, 0, -5864, -23244]\) | \(5445273626857/3103398144\) | \(12711518797824\) | \([2]\) | \(110592\) | \(1.2043\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62832.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 62832.bk do not have complex multiplication.Modular form 62832.2.a.bk
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.
