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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 303240.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 303240.bp1 | 303240bp5 | \([0, 1, 0, -3783400, 2831186288]\) | \(62161150998242/1607445\) | \(154877268344924160\) | \([2]\) | \(7077888\) | \(2.4051\) | |
| 303240.bp2 | 303240bp3 | \([0, 1, 0, -245600, 40569648]\) | \(34008619684/4862025\) | \(234227967558681600\) | \([2, 2]\) | \(3538944\) | \(2.0586\) | |
| 303240.bp3 | 303240bp2 | \([0, 1, 0, -65100, -5782752]\) | \(2533446736/275625\) | \(3319557363360000\) | \([2, 2]\) | \(1769472\) | \(1.7120\) | |
| 303240.bp4 | 303240bp1 | \([0, 1, 0, -63295, -6150250]\) | \(37256083456/525\) | \(395185400400\) | \([2]\) | \(884736\) | \(1.3654\) | \(\Gamma_0(N)\)-optimal |
| 303240.bp5 | 303240bp4 | \([0, 1, 0, 86520, -28586400]\) | \(1486779836/8203125\) | \(-395185400400000000\) | \([2]\) | \(3538944\) | \(2.0586\) | |
| 303240.bp6 | 303240bp6 | \([0, 1, 0, 404200, 219394608]\) | \(75798394558/259416045\) | \(-24994726671484200960\) | \([2]\) | \(7077888\) | \(2.4051\) |
Rank
sage: E.rank()
The elliptic curves in class 303240.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 303240.bp do not have complex multiplication.Modular form 303240.2.a.bp
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
