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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 117117.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117117.bd1 | 117117bp2 | \([0, 0, 1, -263640, 45676179]\) | \(3407872000/456533\) | \(271485427079463597\) | \([3]\) | \(1078272\) | \(2.0728\) | |
| 117117.bd2 | 117117bp1 | \([0, 0, 1, -65910, -6504768]\) | \(53248000/77\) | \(45789412561893\) | \([]\) | \(359424\) | \(1.5235\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 117117.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 117117.bd do not have complex multiplication.Modular form 117117.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
