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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 33600ep
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.n3 | 33600ep1 | \([0, -1, 0, -132508, -17266238]\) | \(257307998572864/19456203375\) | \(19456203375000000\) | \([2]\) | \(221184\) | \(1.8707\) | \(\Gamma_0(N)\)-optimal |
| 33600.n2 | 33600ep2 | \([0, -1, 0, -432633, 89278137]\) | \(139927692143296/27348890625\) | \(1750329000000000000\) | \([2, 2]\) | \(442368\) | \(2.2173\) | |
| 33600.n4 | 33600ep3 | \([0, -1, 0, 890367, 527191137]\) | \(152461584507448/322998046875\) | \(-165375000000000000000\) | \([2]\) | \(884736\) | \(2.5639\) | |
| 33600.n1 | 33600ep4 | \([0, -1, 0, -6557633, 6465403137]\) | \(60910917333827912/3255076125\) | \(1666598976000000000\) | \([2]\) | \(884736\) | \(2.5639\) |
Rank
sage: E.rank()
The elliptic curves in class 33600ep have rank \(0\).
Complex multiplication
The elliptic curves in class 33600ep do not have complex multiplication.Modular form 33600.2.a.ep
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
