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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 126350ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126350.u2 | 126350ba1 | \([1, -1, 0, -8412992, -7493899584]\) | \(104487111/21952\) | \(13835235042274625000000\) | \([2]\) | \(8208000\) | \(2.9632\) | \(\Gamma_0(N)\)-optimal |
126350.u1 | 126350ba2 | \([1, -1, 0, -42707992, 100844005416]\) | \(13669062471/941192\) | \(593185702437524546875000\) | \([2]\) | \(16416000\) | \(3.3098\) |
Rank
sage: E.rank()
The elliptic curves in class 126350ba have rank \(0\).
Complex multiplication
The elliptic curves in class 126350ba do not have complex multiplication.Modular form 126350.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.