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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 440818.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
440818.w1 | 440818w2 | \([1, 0, 0, -466705134, -3880749124084]\) | \(2337944550222313/4769464\) | \(22934370055209523762936\) | \([]\) | \(152295552\) | \(3.5410\) | |
440818.w2 | 440818w1 | \([1, 0, 0, -7535689, -1777486613]\) | \(9841819033/5411854\) | \(26023356570207025782046\) | \([]\) | \(50765184\) | \(2.9917\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 440818.w have rank \(0\).
Complex multiplication
The elliptic curves in class 440818.w do not have complex multiplication.Modular form 440818.2.a.w
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.