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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 69300ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69300.g2 | 69300ba1 | \([0, 0, 0, 58200, -13529500]\) | \(7476617216/31444875\) | \(-91693255500000000\) | \([]\) | \(497664\) | \(1.9373\) | \(\Gamma_0(N)\)-optimal |
69300.g1 | 69300ba2 | \([0, 0, 0, -535800, 414744500]\) | \(-5833703071744/22107421875\) | \(-64465242187500000000\) | \([]\) | \(1492992\) | \(2.4867\) |
Rank
sage: E.rank()
The elliptic curves in class 69300ba have rank \(1\).
Complex multiplication
The elliptic curves in class 69300ba do not have complex multiplication.Modular form 69300.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.