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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 152460.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152460.bc1 | 152460l4 | \([0, 0, 0, -54010407, 80553219406]\) | \(52702650535889104/22020583921875\) | \(7280352971207157996000000\) | \([2]\) | \(29859840\) | \(3.4677\) | |
| 152460.bc2 | 152460l2 | \([0, 0, 0, -46561647, 122289876214]\) | \(33766427105425744/9823275\) | \(3247729923373689600\) | \([2]\) | \(9953280\) | \(2.9184\) | |
| 152460.bc3 | 152460l1 | \([0, 0, 0, -2898192, 1927196161]\) | \(-130287139815424/2250652635\) | \(-46506332599167173040\) | \([2]\) | \(4976640\) | \(2.5718\) | \(\Gamma_0(N)\)-optimal |
| 152460.bc4 | 152460l3 | \([0, 0, 0, 11215248, 9235488229]\) | \(7549996227362816/6152409907875\) | \(-127130245250860853694000\) | \([2]\) | \(14929920\) | \(3.1211\) |
Rank
sage: E.rank()
The elliptic curves in class 152460.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 152460.bc do not have complex multiplication.Modular form 152460.2.a.bc
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
