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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 102921.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102921.l1 | 102921e4 | \([1, 1, 0, -34581459, 78258791538]\) | \(947531277805646290177/38367\) | \(185190180903\) | \([2]\) | \(3538944\) | \(2.5731\) | |
| 102921.l2 | 102921e6 | \([1, 1, 0, -7177264, -6019352867]\) | \(8471112631466271697/1662662681263647\) | \(8025355193887502712423\) | \([2]\) | \(7077888\) | \(2.9197\) | |
| 102921.l3 | 102921e3 | \([1, 1, 0, -2202749, 1172800920]\) | \(244883173420511137/18418027974129\) | \(88900303187777624361\) | \([2, 2]\) | \(3538944\) | \(2.5731\) | |
| 102921.l4 | 102921e2 | \([1, 1, 0, -2161344, 1222114275]\) | \(231331938231569617/1472026689\) | \(7105191670705401\) | \([2, 2]\) | \(1769472\) | \(2.2266\) | |
| 102921.l5 | 102921e1 | \([1, 1, 0, -132499, 19820728]\) | \(-53297461115137/4513839183\) | \(-21787439593057047\) | \([2]\) | \(884736\) | \(1.8800\) | \(\Gamma_0(N)\)-optimal |
| 102921.l6 | 102921e5 | \([1, 1, 0, 2109286, 5209728087]\) | \(215015459663151503/2552757445339983\) | \(-12321672611984038004247\) | \([2]\) | \(7077888\) | \(2.9197\) |
Rank
sage: E.rank()
The elliptic curves in class 102921.l have rank \(0\).
Complex multiplication
The elliptic curves in class 102921.l do not have complex multiplication.Modular form 102921.2.a.l
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
