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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 277725.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277725.t1 | 277725t4 | \([1, 1, 1, -56781813, -164711673594]\) | \(8753151307882969/65205\) | \(150823127222578125\) | \([2]\) | \(17842176\) | \(2.8908\) | |
| 277725.t2 | 277725t2 | \([1, 1, 1, -3551188, -2571189844]\) | \(2141202151369/5832225\) | \(13490290823797265625\) | \([2, 2]\) | \(8921088\) | \(2.5442\) | |
| 277725.t3 | 277725t3 | \([1, 1, 1, -2162563, -4601359594]\) | \(-483551781049/3672913125\) | \(-8495671244986611328125\) | \([2]\) | \(17842176\) | \(2.8908\) | |
| 277725.t4 | 277725t1 | \([1, 1, 1, -311063, -5010844]\) | \(1439069689/828345\) | \(1916012319901640625\) | \([4]\) | \(4460544\) | \(2.1977\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277725.t have rank \(1\).
Complex multiplication
The elliptic curves in class 277725.t do not have complex multiplication.Modular form 277725.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
