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SageMath
E = EllipticCurve("il1")
E.isogeny_class()
Elliptic curves in class 176400.il
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.il1 | 176400jy4 | \([0, 0, 0, -22127175, -40060770750]\) | \(129348709488/6125\) | \(56734289041500000000\) | \([2]\) | \(7962624\) | \(2.8643\) | |
| 176400.il2 | 176400jy3 | \([0, 0, 0, -1455300, -556817625]\) | \(588791808/109375\) | \(63319519019531250000\) | \([2]\) | \(3981312\) | \(2.5177\) | |
| 176400.il3 | 176400jy2 | \([0, 0, 0, -518175, 57538250]\) | \(1210991472/588245\) | \(7474295088540000000\) | \([2]\) | \(2654208\) | \(2.3150\) | |
| 176400.il4 | 176400jy1 | \([0, 0, 0, -426300, 107058875]\) | \(10788913152/8575\) | \(6809671181250000\) | \([2]\) | \(1327104\) | \(1.9684\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.il have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.il do not have complex multiplication.Modular form 176400.2.a.il
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
