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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 10304.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10304.ba1 | 10304t2 | \([0, -1, 0, -10689, -399007]\) | \(1030541881826/62236321\) | \(8157439066112\) | \([2]\) | \(15360\) | \(1.2299\) | |
10304.ba2 | 10304t1 | \([0, -1, 0, -10529, -412351]\) | \(1969910093092/7889\) | \(517013504\) | \([2]\) | \(7680\) | \(0.88336\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10304.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 10304.ba do not have complex multiplication.Modular form 10304.2.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.