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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 202300.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
202300.f1 | 202300g2 | \([0, 1, 0, -28418, -1855487]\) | \(-262885120/343\) | \(-3311674466800\) | \([]\) | \(559872\) | \(1.3094\) | |
202300.f2 | 202300g1 | \([0, 1, 0, 482, -11667]\) | \(1280/7\) | \(-67585193200\) | \([]\) | \(186624\) | \(0.76012\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 202300.f have rank \(1\).
Complex multiplication
The elliptic curves in class 202300.f do not have complex multiplication.Modular form 202300.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.