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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 135531.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
135531.t1 | 135531u2 | \([1, -1, 0, -22845, 1327438]\) | \(19034163/121\) | \(8382228178203\) | \([2]\) | \(405504\) | \(1.3168\) | |
135531.t2 | 135531u1 | \([1, -1, 0, -2310, -7337]\) | \(19683/11\) | \(762020743473\) | \([2]\) | \(202752\) | \(0.97019\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 135531.t have rank \(1\).
Complex multiplication
The elliptic curves in class 135531.t do not have complex multiplication.Modular form 135531.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.