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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 380926ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
380926.ba2 | 380926ba1 | \([1, 1, 0, 45965, 5151021]\) | \(45408227375/74381632\) | \(-17592270607842112\) | \([]\) | \(3048192\) | \(1.8023\) | \(\Gamma_0(N)\)-optimal |
380926.ba1 | 380926ba2 | \([1, 1, 0, -1491935, 703788233]\) | \(-1552807715412625/7697866228\) | \(-1820650369515216148\) | \([]\) | \(9144576\) | \(2.3516\) |
Rank
sage: E.rank()
The elliptic curves in class 380926ba have rank \(0\).
Complex multiplication
The elliptic curves in class 380926ba do not have complex multiplication.Modular form 380926.2.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.