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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 152592f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152592.bu2 | 152592f1 | \([0, 1, 0, -55584, -4106508]\) | \(192100033/38148\) | \(3771596727140352\) | \([2]\) | \(663552\) | \(1.7052\) | \(\Gamma_0(N)\)-optimal |
152592.bu1 | 152592f2 | \([0, 1, 0, -841664, -297471564]\) | \(666940371553/37026\) | \(3660667411636224\) | \([2]\) | \(1327104\) | \(2.0517\) |
Rank
sage: E.rank()
The elliptic curves in class 152592f have rank \(1\).
Complex multiplication
The elliptic curves in class 152592f do not have complex multiplication.Modular form 152592.2.a.f
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.