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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 24150.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24150.f1 | 24150q1 | \([1, 1, 0, -98325, 982125]\) | \(53826041237093/30917811456\) | \(60386350500000000\) | \([2]\) | \(215040\) | \(1.9096\) | \(\Gamma_0(N)\)-optimal |
24150.f2 | 24150q2 | \([1, 1, 0, 391675, 8332125]\) | \(3402275649500827/1983669431184\) | \(-3874354357781250000\) | \([2]\) | \(430080\) | \(2.2562\) |
Rank
sage: E.rank()
The elliptic curves in class 24150.f have rank \(1\).
Complex multiplication
The elliptic curves in class 24150.f do not have complex multiplication.Modular form 24150.2.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 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.