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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 259920.fl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259920.fl1 | 259920fl2 | \([0, 0, 0, -4601667, -3803616574]\) | \(-27692833539889/35156250\) | \(-13680577296000000000\) | \([]\) | \(7464960\) | \(2.5802\) | |
259920.fl2 | 259920fl1 | \([0, 0, 0, 76893, -24275806]\) | \(129205871/729000\) | \(-283680450809856000\) | \([]\) | \(2488320\) | \(2.0309\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259920.fl have rank \(0\).
Complex multiplication
The elliptic curves in class 259920.fl do not have complex multiplication.Modular form 259920.2.a.fl
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.