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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 121275.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121275.bb1 | 121275dj4 | \([1, -1, 1, -113190230, 463540877272]\) | \(119678115308998401/1925\) | \(2579684108203125\) | \([2]\) | \(9437184\) | \(2.9559\) | |
| 121275.bb2 | 121275dj3 | \([1, -1, 1, -7680980, 5929068772]\) | \(37397086385121/10316796875\) | \(13825494517401123046875\) | \([2]\) | \(9437184\) | \(2.9559\) | |
| 121275.bb3 | 121275dj2 | \([1, -1, 1, -7074605, 7243689772]\) | \(29220958012401/3705625\) | \(4965891908291015625\) | \([2, 2]\) | \(4718592\) | \(2.6093\) | |
| 121275.bb4 | 121275dj1 | \([1, -1, 1, -404480, 133336522]\) | \(-5461074081/2562175\) | \(-3433559548018359375\) | \([2]\) | \(2359296\) | \(2.2627\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 121275.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 121275.bb do not have complex multiplication.Modular form 121275.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
