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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 338130.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338130.s1 | 338130s2 | \([1, -1, 0, -2889765, -1887376775]\) | \(30870492353/50700\) | \(4383043491692069100\) | \([2]\) | \(8912896\) | \(2.4734\) | |
338130.s2 | 338130s1 | \([1, -1, 0, -236745, -9569219]\) | \(16974593/9360\) | \(809177260004689680\) | \([2]\) | \(4456448\) | \(2.1268\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 338130.s have rank \(1\).
Complex multiplication
The elliptic curves in class 338130.s do not have complex multiplication.Modular form 338130.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.