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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 59248.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59248.n1 | 59248c4 | \([0, 0, 0, -158171, 24212330]\) | \(1443468546/7\) | \(2122242504704\) | \([2]\) | \(202752\) | \(1.5657\) | |
| 59248.n2 | 59248c3 | \([0, 0, 0, -31211, -1679046]\) | \(11090466/2401\) | \(727929179113472\) | \([2]\) | \(202752\) | \(1.5657\) | |
| 59248.n3 | 59248c2 | \([0, 0, 0, -10051, 365010]\) | \(740772/49\) | \(7427848766464\) | \([2, 2]\) | \(101376\) | \(1.2191\) | |
| 59248.n4 | 59248c1 | \([0, 0, 0, 529, 24334]\) | \(432/7\) | \(-265280313088\) | \([2]\) | \(50688\) | \(0.87257\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59248.n have rank \(0\).
Complex multiplication
The elliptic curves in class 59248.n do not have complex multiplication.Modular form 59248.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
