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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 3150.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3150.ba1 | 3150bf7 | \([1, -1, 1, -1451480, -423093603]\) | \(29689921233686449/10380965400750\) | \(118245684017917968750\) | \([2]\) | \(110592\) | \(2.5531\) | |
| 3150.ba2 | 3150bf4 | \([1, -1, 1, -1296230, -567705603]\) | \(21145699168383889/2593080\) | \(29536801875000\) | \([2]\) | \(36864\) | \(2.0037\) | |
| 3150.ba3 | 3150bf6 | \([1, -1, 1, -607730, 177656397]\) | \(2179252305146449/66177562500\) | \(753803797851562500\) | \([2, 2]\) | \(55296\) | \(2.2065\) | |
| 3150.ba4 | 3150bf3 | \([1, -1, 1, -603230, 180482397]\) | \(2131200347946769/2058000\) | \(23441906250000\) | \([4]\) | \(27648\) | \(1.8599\) | |
| 3150.ba5 | 3150bf2 | \([1, -1, 1, -81230, -8805603]\) | \(5203798902289/57153600\) | \(651015225000000\) | \([2, 2]\) | \(18432\) | \(1.6572\) | |
| 3150.ba6 | 3150bf5 | \([1, -1, 1, -18230, -22161603]\) | \(-58818484369/18600435000\) | \(-211870579921875000\) | \([2]\) | \(36864\) | \(2.0037\) | |
| 3150.ba7 | 3150bf1 | \([1, -1, 1, -9230, 122397]\) | \(7633736209/3870720\) | \(44089920000000\) | \([4]\) | \(9216\) | \(1.3106\) | \(\Gamma_0(N)\)-optimal |
| 3150.ba8 | 3150bf8 | \([1, -1, 1, 164020, 597488397]\) | \(42841933504271/13565917968750\) | \(-154524284362792968750\) | \([2]\) | \(110592\) | \(2.5531\) |
Rank
sage: E.rank()
The elliptic curves in class 3150.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 3150.ba do not have complex multiplication.Modular form 3150.2.a.ba
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
