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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 2880bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2880.q8 | 2880bb1 | \([0, 0, 0, 852, 29392]\) | \(357911/2160\) | \(-412782428160\) | \([2]\) | \(3072\) | \(0.91074\) | \(\Gamma_0(N)\)-optimal |
| 2880.q6 | 2880bb2 | \([0, 0, 0, -10668, 384208]\) | \(702595369/72900\) | \(13931406950400\) | \([2, 2]\) | \(6144\) | \(1.2573\) | |
| 2880.q7 | 2880bb3 | \([0, 0, 0, -7788, -865712]\) | \(-273359449/1536000\) | \(-293534171136000\) | \([2]\) | \(9216\) | \(1.4600\) | |
| 2880.q5 | 2880bb4 | \([0, 0, 0, -39468, -2599472]\) | \(35578826569/5314410\) | \(1015599566684160\) | \([2]\) | \(12288\) | \(1.6039\) | |
| 2880.q4 | 2880bb5 | \([0, 0, 0, -166188, 26076112]\) | \(2656166199049/33750\) | \(6449725440000\) | \([2]\) | \(12288\) | \(1.6039\) | |
| 2880.q3 | 2880bb6 | \([0, 0, 0, -192108, -32347568]\) | \(4102915888729/9000000\) | \(1719926784000000\) | \([2, 2]\) | \(18432\) | \(1.8066\) | |
| 2880.q1 | 2880bb7 | \([0, 0, 0, -3072108, -2072539568]\) | \(16778985534208729/81000\) | \(15479341056000\) | \([2]\) | \(36864\) | \(2.1532\) | |
| 2880.q2 | 2880bb8 | \([0, 0, 0, -261228, -6994352]\) | \(10316097499609/5859375000\) | \(1119744000000000000\) | \([2]\) | \(36864\) | \(2.1532\) |
Rank
sage: E.rank()
The elliptic curves in class 2880bb have rank \(1\).
Complex multiplication
The elliptic curves in class 2880bb do not have complex multiplication.Modular form 2880.2.a.bb
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
