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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 70805.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70805.bd1 | 70805e3 | \([0, 1, 1, -1859811, 1020602020]\) | \(-250523582464/13671875\) | \(-38824855443294921875\) | \([]\) | \(1451520\) | \(2.5170\) | |
| 70805.bd2 | 70805e1 | \([0, 1, 1, -18881, -1114130]\) | \(-262144/35\) | \(-99391629934835\) | \([]\) | \(161280\) | \(1.4184\) | \(\Gamma_0(N)\)-optimal |
| 70805.bd3 | 70805e2 | \([0, 1, 1, 122729, 2865111]\) | \(71991296/42875\) | \(-121754746670172875\) | \([]\) | \(483840\) | \(1.9677\) |
Rank
sage: E.rank()
The elliptic curves in class 70805.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 70805.bd do not have complex multiplication.Modular form 70805.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
