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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 33327.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33327.k1 | 33327m6 | \([1, -1, 0, -3732723, -2774857986]\) | \(53297461115137/147\) | \(15863969972907\) | \([2]\) | \(405504\) | \(2.1913\) | |
| 33327.k2 | 33327m4 | \([1, -1, 0, -233388, -43277085]\) | \(13027640977/21609\) | \(2332003586017329\) | \([2, 2]\) | \(202752\) | \(1.8447\) | |
| 33327.k3 | 33327m3 | \([1, -1, 0, -185778, 30680289]\) | \(6570725617/45927\) | \(4956357475821087\) | \([2]\) | \(202752\) | \(1.8447\) | |
| 33327.k4 | 33327m5 | \([1, -1, 0, -161973, -70314804]\) | \(-4354703137/17294403\) | \(-1866380203342535643\) | \([2]\) | \(405504\) | \(2.1913\) | |
| 33327.k5 | 33327m2 | \([1, -1, 0, -19143, -213840]\) | \(7189057/3969\) | \(428327189268489\) | \([2, 2]\) | \(101376\) | \(1.4981\) | |
| 33327.k6 | 33327m1 | \([1, -1, 0, 4662, -28161]\) | \(103823/63\) | \(-6798844274103\) | \([2]\) | \(50688\) | \(1.1515\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33327.k have rank \(0\).
Complex multiplication
The elliptic curves in class 33327.k do not have complex multiplication.Modular form 33327.2.a.k
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
