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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 159936.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159936.ba1 | 159936im3 | \([0, -1, 0, -263489, 9384705]\) | \(524776831496/294004851\) | \(1133424696206917632\) | \([2]\) | \(2162688\) | \(2.1545\) | |
159936.ba2 | 159936im2 | \([0, -1, 0, -163529, -25261431]\) | \(1003604321728/6245001\) | \(3009405430370304\) | \([2, 2]\) | \(1081344\) | \(1.8079\) | |
159936.ba3 | 159936im1 | \([0, -1, 0, -163284, -25341546]\) | \(63942417278272/2499\) | \(18816310464\) | \([2]\) | \(540672\) | \(1.4614\) | \(\Gamma_0(N)\)-optimal |
159936.ba4 | 159936im4 | \([0, -1, 0, -67489, -54784127]\) | \(-8818423496/331494849\) | \(-1277953228472352768\) | \([2]\) | \(2162688\) | \(2.1545\) |
Rank
sage: E.rank()
The elliptic curves in class 159936.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 159936.ba do not have complex multiplication.Modular form 159936.2.a.ba
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.