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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 15246.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15246.t1 | 15246l3 | \([1, -1, 0, -246681, -47076485]\) | \(1285429208617/614922\) | \(794152066433418\) | \([2]\) | \(122880\) | \(1.8139\) | |
| 15246.t2 | 15246l4 | \([1, -1, 0, -137781, 19391719]\) | \(223980311017/4278582\) | \(5525651605739958\) | \([2]\) | \(122880\) | \(1.8139\) | |
| 15246.t3 | 15246l2 | \([1, -1, 0, -17991, -469463]\) | \(498677257/213444\) | \(275656089175236\) | \([2, 2]\) | \(61440\) | \(1.4673\) | |
| 15246.t4 | 15246l1 | \([1, -1, 0, 3789, -55643]\) | \(4657463/3696\) | \(-4773265613424\) | \([2]\) | \(30720\) | \(1.1208\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15246.t have rank \(1\).
Complex multiplication
The elliptic curves in class 15246.t do not have complex multiplication.Modular form 15246.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
