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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 21175.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
21175.ba1 | 21175h2 | \([1, 0, 1, -155851, -21873777]\) | \(15124197817/1294139\) | \(35822596577796875\) | \([2]\) | \(184320\) | \(1.9176\) | |
21175.ba2 | 21175h1 | \([1, 0, 1, 10524, -1576027]\) | \(4657463/41503\) | \(-1148829627859375\) | \([2]\) | \(92160\) | \(1.5711\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 21175.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 21175.ba do not have complex multiplication.Modular form 21175.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.