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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 145200.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145200.n1 | 145200jr4 | \([0, -1, 0, -4889408, -3951230688]\) | \(228027144098/12890625\) | \(730768912500000000000\) | \([2]\) | \(8847360\) | \(2.7580\) | |
| 145200.n2 | 145200jr2 | \([0, -1, 0, -896408, 249405312]\) | \(2810381476/680625\) | \(19292299290000000000\) | \([2, 2]\) | \(4423680\) | \(2.4114\) | |
| 145200.n3 | 145200jr1 | \([0, -1, 0, -835908, 294417312]\) | \(9115564624/825\) | \(5846151300000000\) | \([2]\) | \(2211840\) | \(2.0649\) | \(\Gamma_0(N)\)-optimal |
| 145200.n4 | 145200jr3 | \([0, -1, 0, 2128592, 1568305312]\) | \(18814587262/29648025\) | \(-1680745114144800000000\) | \([2]\) | \(8847360\) | \(2.7580\) |
Rank
sage: E.rank()
The elliptic curves in class 145200.n have rank \(2\).
Complex multiplication
The elliptic curves in class 145200.n do not have complex multiplication.Modular form 145200.2.a.n
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.
