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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 44400bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44400.s2 | 44400bd1 | \([0, -1, 0, -333, 2412]\) | \(16384000/333\) | \(83250000\) | \([2]\) | \(13824\) | \(0.31068\) | \(\Gamma_0(N)\)-optimal |
44400.s1 | 44400bd2 | \([0, -1, 0, -708, -3588]\) | \(9826000/4107\) | \(16428000000\) | \([2]\) | \(27648\) | \(0.65725\) |
Rank
sage: E.rank()
The elliptic curves in class 44400bd have rank \(1\).
Complex multiplication
The elliptic curves in class 44400bd do not have complex multiplication.Modular form 44400.2.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 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.