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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 320790ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
320790.ba1 | 320790ba1 | \([1, 0, 1, -2174, 38846]\) | \(-13596259609/9990\) | \(-834374790\) | \([3]\) | \(277344\) | \(0.64598\) | \(\Gamma_0(N)\)-optimal |
320790.ba2 | 320790ba2 | \([1, 0, 1, 2161, 167162]\) | \(13371532631/151959000\) | \(-12691767639000\) | \([]\) | \(832032\) | \(1.1953\) |
Rank
sage: E.rank()
The elliptic curves in class 320790ba have rank \(0\).
Complex multiplication
The elliptic curves in class 320790ba do not have complex multiplication.Modular form 320790.2.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.