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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 100800.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.b1 | 100800p1 | \([0, 0, 0, -5400, -135000]\) | \(55296/7\) | \(2204496000000\) | \([2]\) | \(196608\) | \(1.0977\) | \(\Gamma_0(N)\)-optimal |
100800.b2 | 100800p2 | \([0, 0, 0, 8100, -702000]\) | \(11664/49\) | \(-246903552000000\) | \([2]\) | \(393216\) | \(1.4443\) |
Rank
sage: E.rank()
The elliptic curves in class 100800.b have rank \(1\).
Complex multiplication
The elliptic curves in class 100800.b do not have complex multiplication.Modular form 100800.2.a.b
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.