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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 33620.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33620.a1 | 33620a3 | \([0, -1, 0, -69481, -7024650]\) | \(488095744/125\) | \(9500208482000\) | \([2]\) | \(103680\) | \(1.4761\) | |
33620.a2 | 33620a4 | \([0, -1, 0, -61076, -8796424]\) | \(-20720464/15625\) | \(-19000416964000000\) | \([2]\) | \(207360\) | \(1.8227\) | |
33620.a3 | 33620a1 | \([0, -1, 0, -2241, 28826]\) | \(16384/5\) | \(380008339280\) | \([2]\) | \(34560\) | \(0.92684\) | \(\Gamma_0(N)\)-optimal |
33620.a4 | 33620a2 | \([0, -1, 0, 6164, 186840]\) | \(21296/25\) | \(-30400667142400\) | \([2]\) | \(69120\) | \(1.2734\) |
Rank
sage: E.rank()
The elliptic curves in class 33620.a have rank \(0\).
Complex multiplication
The elliptic curves in class 33620.a do not have complex multiplication.Modular form 33620.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.