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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 265598.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
265598.a1 | 265598a3 | \([1, 1, 0, -8768971, -9998373187]\) | \(15698803397448457/20709376\) | \(98371694766063616\) | \([]\) | \(7776000\) | \(2.5366\) | |
265598.a2 | 265598a2 | \([1, 1, 0, -137036, -5912432]\) | \(59914169497/31554496\) | \(149887145272217536\) | \([]\) | \(2592000\) | \(1.9873\) | |
265598.a3 | 265598a1 | \([1, 1, 0, -78201, 8384473]\) | \(11134383337/316\) | \(1501032940156\) | \([]\) | \(864000\) | \(1.4380\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 265598.a have rank \(1\).
Complex multiplication
The elliptic curves in class 265598.a do not have complex multiplication.Modular form 265598.2.a.a
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.