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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 53361.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality | CM discriminant |
---|---|---|---|---|---|---|---|---|---|
53361.bb1 | 53361b1 | \([0, 0, 1, 0, -6603]\) | \(0\) | \(-18833604867\) | \([]\) | \(26208\) | \(0.65046\) | \(\Gamma_0(N)\)-optimal | \(-3\) |
53361.bb2 | 53361b2 | \([0, 0, 1, 0, 178274]\) | \(0\) | \(-13729697948043\) | \([]\) | \(78624\) | \(1.1998\) | \(-3\) |
Rank
sage: E.rank()
The elliptic curves in class 53361.bb have rank \(0\).
Complex multiplication
Each elliptic curve in class 53361.bb has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).Modular form 53361.2.a.bb
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.