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SageMath
E = EllipticCurve("jt1")
E.isogeny_class()
Elliptic curves in class 145200jt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145200.q1 | 145200jt1 | \([0, -1, 0, -1283, -16938]\) | \(702464/15\) | \(4991250000\) | \([2]\) | \(110592\) | \(0.64996\) | \(\Gamma_0(N)\)-optimal |
145200.q2 | 145200jt2 | \([0, -1, 0, 92, -52688]\) | \(16/225\) | \(-1197900000000\) | \([2]\) | \(221184\) | \(0.99654\) |
Rank
sage: E.rank()
The elliptic curves in class 145200jt have rank \(1\).
Complex multiplication
The elliptic curves in class 145200jt do not have complex multiplication.Modular form 145200.2.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.