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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 18150.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18150.g1 | 18150c1 | \([1, 1, 0, -4167000, -3274506000]\) | \(217190179331/97200\) | \(3581133055706250000\) | \([2]\) | \(506880\) | \(2.5183\) | \(\Gamma_0(N)\)-optimal |
18150.g2 | 18150c2 | \([1, 1, 0, -3501500, -4354612500]\) | \(-128864147651/147622500\) | \(-5438845828353867187500\) | \([2]\) | \(1013760\) | \(2.8649\) |
Rank
sage: E.rank()
The elliptic curves in class 18150.g have rank \(1\).
Complex multiplication
The elliptic curves in class 18150.g do not have complex multiplication.Modular form 18150.2.a.g
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.