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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 185900.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185900.be1 | 185900be1 | \([0, -1, 0, -7526133, 7958049137]\) | \(-2441851961344/3020875\) | \(-58324746551500000000\) | \([]\) | \(6967296\) | \(2.7022\) | \(\Gamma_0(N)\)-optimal |
185900.be2 | 185900be2 | \([0, -1, 0, 10049867, 36874963137]\) | \(5814126903296/33794921875\) | \(-652486532242187500000000\) | \([]\) | \(20901888\) | \(3.2515\) |
Rank
sage: E.rank()
The elliptic curves in class 185900.be have rank \(1\).
Complex multiplication
The elliptic curves in class 185900.be do not have complex multiplication.Modular form 185900.2.a.be
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.