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SageMath
E = EllipticCurve("jt1")
E.isogeny_class()
Elliptic curves in class 352800jt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
352800.jt1 | 352800jt1 | \([0, 0, 0, -2318925, -1122982000]\) | \(16079333824/2953125\) | \(253278076078125000000\) | \([2]\) | \(10616832\) | \(2.6336\) | \(\Gamma_0(N)\)-optimal |
352800.jt2 | 352800jt2 | \([0, 0, 0, 4571700, -6525232000]\) | \(1925134784/4465125\) | \(-24509212865928000000000\) | \([2]\) | \(21233664\) | \(2.9801\) |
Rank
sage: E.rank()
The elliptic curves in class 352800jt have rank \(1\).
Complex multiplication
The elliptic curves in class 352800jt do not have complex multiplication.Modular form 352800.2.a.jt
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.