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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 132600.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
132600.m1 | 132600ca2 | \([0, -1, 0, -780753208, 7975762062412]\) | \(13158459661252114525066/745117393587651747\) | \(2980469574350606988000000000\) | \([2]\) | \(51968000\) | \(4.0264\) | |
132600.m2 | 132600ca1 | \([0, -1, 0, -769818208, 8221340292412]\) | \(25226572870537521199412/88284716200629\) | \(176569432401258000000000\) | \([2]\) | \(25984000\) | \(3.6798\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 132600.m have rank \(1\).
Complex multiplication
The elliptic curves in class 132600.m do not have complex multiplication.Modular form 132600.2.a.m
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.