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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 143745.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
143745.t1 | 143745o2 | \([0, 1, 1, -57251, -5290795]\) | \(15159227841150976/3026520525\) | \(4143306598725\) | \([]\) | \(435456\) | \(1.4196\) | |
143745.t2 | 143745o1 | \([0, 1, 1, -1751, 17780]\) | \(433937022976/144703125\) | \(198098578125\) | \([]\) | \(145152\) | \(0.87030\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 143745.t have rank \(1\).
Complex multiplication
The elliptic curves in class 143745.t do not have complex multiplication.Modular form 143745.2.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 LMFDB 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 LMFDB labels.