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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 54720.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54720.bj1 | 54720bc4 | \([0, 0, 0, -357708, 82226032]\) | \(26487576322129/44531250\) | \(8510054400000000\) | \([2]\) | \(393216\) | \(1.9519\) | |
| 54720.bj2 | 54720bc2 | \([0, 0, 0, -29388, 408688]\) | \(14688124849/8122500\) | \(1552233922560000\) | \([2, 2]\) | \(196608\) | \(1.6054\) | |
| 54720.bj3 | 54720bc1 | \([0, 0, 0, -17868, -913808]\) | \(3301293169/22800\) | \(4357147852800\) | \([2]\) | \(98304\) | \(1.2588\) | \(\Gamma_0(N)\)-optimal |
| 54720.bj4 | 54720bc3 | \([0, 0, 0, 114612, 3231088]\) | \(871257511151/527800050\) | \(-100864160287948800\) | \([2]\) | \(393216\) | \(1.9519\) |
Rank
sage: E.rank()
The elliptic curves in class 54720.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 54720.bj do not have complex multiplication.Modular form 54720.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
