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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 96800bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96800.j2 | 96800bz1 | \([0, 1, 0, -12615258, 17241906988]\) | \(125330290485184/378125\) | \(669871503125000000\) | \([2]\) | \(2764800\) | \(2.6482\) | \(\Gamma_0(N)\)-optimal |
| 96800.j1 | 96800bz2 | \([0, 1, 0, -12781633, 16763578863]\) | \(2036792051776/107421875\) | \(12179481875000000000000\) | \([2]\) | \(5529600\) | \(2.9948\) |
Rank
sage: E.rank()
The elliptic curves in class 96800bz have rank \(1\).
Complex multiplication
The elliptic curves in class 96800bz do not have complex multiplication.Modular form 96800.2.a.bz
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 Cremona 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 Cremona labels.
