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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 290145y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
290145.y4 | 290145y1 | \([1, 0, 1, -4415268, -3475856867]\) | \(16003198512756001/488525390625\) | \(290586295244384765625\) | \([2]\) | \(10321920\) | \(2.7025\) | \(\Gamma_0(N)\)-optimal |
290145.y2 | 290145y2 | \([1, 0, 1, -70118393, -225999200617]\) | \(64096096056024006001/62562515625\) | \(37213643314176890625\) | \([2, 2]\) | \(20643840\) | \(3.0491\) | |
290145.y3 | 290145y3 | \([1, 0, 1, -69592768, -229554107617]\) | \(-62665433378363916001/2004003001000125\) | \(-1192027720348860673915125\) | \([2]\) | \(41287680\) | \(3.3956\) | |
290145.y1 | 290145y4 | \([1, 0, 1, -1121894018, -14463675481117]\) | \(262537424941059264096001/250125\) | \(148780183165125\) | \([2]\) | \(41287680\) | \(3.3956\) |
Rank
sage: E.rank()
The elliptic curves in class 290145y have rank \(1\).
Complex multiplication
The elliptic curves in class 290145y do not have complex multiplication.Modular form 290145.2.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.