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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 145200.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145200.bv1 | 145200dq4 | \([0, -1, 0, -1603048, 779201392]\) | \(502270291349/1889568\) | \(1713912307531776000\) | \([2]\) | \(2688000\) | \(2.3581\) | |
| 145200.bv2 | 145200dq2 | \([0, -1, 0, -102648, -12622608]\) | \(131872229/18\) | \(16326706176000\) | \([2]\) | \(537600\) | \(1.5534\) | |
| 145200.bv3 | 145200dq3 | \([0, -1, 0, -54248, 23386992]\) | \(-19465109/248832\) | \(-225700386177024000\) | \([2]\) | \(1344000\) | \(2.0115\) | |
| 145200.bv4 | 145200dq1 | \([0, -1, 0, -5848, -232208]\) | \(-24389/12\) | \(-10884470784000\) | \([2]\) | \(268800\) | \(1.2068\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 145200.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 145200.bv do not have complex multiplication.Modular form 145200.2.a.bv
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
