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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 27200t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27200.ca2 | 27200t1 | \([0, 1, 0, 47, -17]\) | \(27440/17\) | \(-6963200\) | \([]\) | \(2304\) | \(0.0021306\) | \(\Gamma_0(N)\)-optimal |
| 27200.ca1 | 27200t2 | \([0, 1, 0, -753, -8497]\) | \(-115431760/4913\) | \(-2012364800\) | \([]\) | \(6912\) | \(0.55144\) |
Rank
sage: E.rank()
The elliptic curves in class 27200t have rank \(0\).
Complex multiplication
The elliptic curves in class 27200t do not have complex multiplication.Modular form 27200.2.a.t
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.
