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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 64974bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64974.bl2 | 64974bd1 | \([1, 1, 1, -109089485, 506551623563]\) | \(-24905087205614147556241/4819348696095929736\) | \(-27782586182602511838022536\) | \([]\) | \(14620032\) | \(3.6057\) | \(\Gamma_0(N)\)-optimal |
64974.bl1 | 64974bd2 | \([1, 1, 1, -4296045895, -145014496259011]\) | \(-1521059241134755603512440881/695595284594977727840256\) | \(-4009968392228412200431235629056\) | \([]\) | \(102340224\) | \(4.5787\) |
Rank
sage: E.rank()
The elliptic curves in class 64974bd have rank \(1\).
Complex multiplication
The elliptic curves in class 64974bd do not have complex multiplication.Modular form 64974.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.