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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 35728y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35728.m4 | 35728y1 | \([0, 0, 0, 9349, -396566]\) | \(22062729659823/29354283343\) | \(-120235144572928\) | \([2]\) | \(86016\) | \(1.3875\) | \(\Gamma_0(N)\)-optimal |
35728.m3 | 35728y2 | \([0, 0, 0, -57931, -3881670]\) | \(5249244962308257/1448621666569\) | \(5933554346266624\) | \([2, 2]\) | \(172032\) | \(1.7341\) | |
35728.m2 | 35728y3 | \([0, 0, 0, -338651, 72754890]\) | \(1048626554636928177/48569076788309\) | \(198938938524913664\) | \([4]\) | \(344064\) | \(2.0807\) | |
35728.m1 | 35728y4 | \([0, 0, 0, -853691, -303564886]\) | \(16798320881842096017/2132227789307\) | \(8733605025001472\) | \([2]\) | \(344064\) | \(2.0807\) |
Rank
sage: E.rank()
The elliptic curves in class 35728y have rank \(1\).
Complex multiplication
The elliptic curves in class 35728y do not have complex multiplication.Modular form 35728.2.a.y
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.