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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 152460.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152460.bd1 | 152460bl3 | \([0, 0, 0, -7239672, 7497644121]\) | \(75216478666752/326095\) | \(181933018855655760\) | \([2]\) | \(3732480\) | \(2.5187\) | |
| 152460.bd2 | 152460bl4 | \([0, 0, 0, -7125327, 7745932854]\) | \(-4481782160112/310023175\) | \(-2767461121107175046400\) | \([2]\) | \(7464960\) | \(2.8653\) | |
| 152460.bd3 | 152460bl1 | \([0, 0, 0, -124872, 1372261]\) | \(281370820608/161767375\) | \(123802893772866000\) | \([2]\) | \(1244160\) | \(1.9694\) | \(\Gamma_0(N)\)-optimal |
| 152460.bd4 | 152460bl2 | \([0, 0, 0, 497673, 10959454]\) | \(1113258734352/648484375\) | \(-7940710387764000000\) | \([2]\) | \(2488320\) | \(2.3160\) |
Rank
sage: E.rank()
The elliptic curves in class 152460.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 152460.bd do not have complex multiplication.Modular form 152460.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
