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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 43560bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43560.bm4 | 43560bf1 | \([0, 0, 0, 3993, -45254]\) | \(21296/15\) | \(-4959237000960\) | \([2]\) | \(92160\) | \(1.1245\) | \(\Gamma_0(N)\)-optimal |
| 43560.bm3 | 43560bf2 | \([0, 0, 0, -17787, -380666]\) | \(470596/225\) | \(297554220057600\) | \([2, 2]\) | \(184320\) | \(1.4711\) | |
| 43560.bm2 | 43560bf3 | \([0, 0, 0, -148467, 21756526]\) | \(136835858/1875\) | \(4959237000960000\) | \([2]\) | \(368640\) | \(1.8177\) | |
| 43560.bm1 | 43560bf4 | \([0, 0, 0, -235587, -43984226]\) | \(546718898/405\) | \(1071195192207360\) | \([2]\) | \(368640\) | \(1.8177\) |
Rank
sage: E.rank()
The elliptic curves in class 43560bf have rank \(0\).
Complex multiplication
The elliptic curves in class 43560bf do not have complex multiplication.Modular form 43560.2.a.bf
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
