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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 60984.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60984.bd1 | 60984bv2 | \([0, 0, 0, -488235, -130286266]\) | \(4866277250/43659\) | \(115474841719953408\) | \([2]\) | \(737280\) | \(2.0968\) | |
| 60984.bd2 | 60984bv1 | \([0, 0, 0, -9075, -4842178]\) | \(-62500/7623\) | \(-10081136975551488\) | \([2]\) | \(368640\) | \(1.7502\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 60984.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 60984.bd do not have complex multiplication.Modular form 60984.2.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.
