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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 435120.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435120.bd1 | 435120bd2 | \([0, -1, 0, -39636, -2872260]\) | \(78427801868848/4424246325\) | \(388484221305600\) | \([2]\) | \(1720320\) | \(1.5541\) | |
435120.bd2 | 435120bd1 | \([0, -1, 0, -7261, 183940]\) | \(7715405037568/1871251875\) | \(10269430290000\) | \([2]\) | \(860160\) | \(1.2076\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435120.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 435120.bd do not have complex multiplication.Modular form 435120.2.a.bd
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.