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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 16830m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16830.v3 | 16830m1 | \([1, -1, 0, -1164, 12348]\) | \(6462919457883/1414187500\) | \(38183062500\) | \([6]\) | \(16128\) | \(0.74413\) | \(\Gamma_0(N)\)-optimal |
| 16830.v4 | 16830m2 | \([1, -1, 0, 2586, 73098]\) | \(70819203762117/127995282250\) | \(-3455872620750\) | \([6]\) | \(32256\) | \(1.0907\) | |
| 16830.v1 | 16830m3 | \([1, -1, 0, -30039, -1995427]\) | \(152298969481827/86468800\) | \(1701965390400\) | \([2]\) | \(48384\) | \(1.2934\) | |
| 16830.v2 | 16830m4 | \([1, -1, 0, -24639, -2739547]\) | \(-84044939142627/116825833960\) | \(-2299482889834680\) | \([2]\) | \(96768\) | \(1.6400\) |
Rank
sage: E.rank()
The elliptic curves in class 16830m have rank \(1\).
Complex multiplication
The elliptic curves in class 16830m do not have complex multiplication.Modular form 16830.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
