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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 416955ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 416955.ba3 | 416955ba1 | \([1, 0, 0, -5863550, 5464497507]\) | \(473897054735271721/779625\) | \(36678144974625\) | \([2]\) | \(7962624\) | \(2.2945\) | \(\Gamma_0(N)\)-optimal |
| 416955.ba2 | 416955ba2 | \([1, 0, 0, -5865355, 5460964400]\) | \(474334834335054841/607815140625\) | \(28595198775842015625\) | \([2, 2]\) | \(15925248\) | \(2.6411\) | |
| 416955.ba4 | 416955ba3 | \([1, 0, 0, -4285980, 8468410275]\) | \(-185077034913624841/551466161890875\) | \(-25944211427844840235875\) | \([2]\) | \(31850496\) | \(2.9877\) | |
| 416955.ba1 | 416955ba4 | \([1, 0, 0, -7473610, 2227406897]\) | \(981281029968144361/522287841796875\) | \(24571491652922607421875\) | \([2]\) | \(31850496\) | \(2.9877\) |
Rank
sage: E.rank()
The elliptic curves in class 416955ba have rank \(1\).
Complex multiplication
The elliptic curves in class 416955ba do not have complex multiplication.Modular form 416955.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
