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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 484242bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
484242.bd1 | 484242bd1 | \([1, 0, 1, -11135, -458350]\) | \(-86175179713/1152576\) | \(-2041858691136\) | \([]\) | \(1944000\) | \(1.1697\) | \(\Gamma_0(N)\)-optimal* |
484242.bd2 | 484242bd2 | \([1, 0, 1, 39685, -2308198]\) | \(3901777377407/3560891556\) | \(-6308336605838916\) | \([]\) | \(5832000\) | \(1.7190\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 484242bd have rank \(0\).
Complex multiplication
The elliptic curves in class 484242bd do not have complex multiplication.Modular form 484242.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.