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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 150075s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
150075.v2 | 150075s1 | \([0, 0, 1, -27904800, -50555649344]\) | \(210966209738334797824/25153051046653125\) | \(286508972078283251953125\) | \([]\) | \(12441600\) | \(3.2320\) | \(\Gamma_0(N)\)-optimal |
150075.v1 | 150075s2 | \([0, 0, 1, -535288800, 4759595300281]\) | \(1489157481162281146384384/2616603057861328125\) | \(29804744205951690673828125\) | \([]\) | \(37324800\) | \(3.7813\) |
Rank
sage: E.rank()
The elliptic curves in class 150075s have rank \(0\).
Complex multiplication
The elliptic curves in class 150075s do not have complex multiplication.Modular form 150075.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.