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SageMath
E = EllipticCurve("ik1")
E.isogeny_class()
Elliptic curves in class 92400.ik
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.ik1 | 92400cq4 | \([0, 1, 0, -176408, 28459188]\) | \(18972782339618/396165\) | \(12677280000000\) | \([2]\) | \(491520\) | \(1.6327\) | |
| 92400.ik2 | 92400cq3 | \([0, 1, 0, -46408, -3440812]\) | \(345431270018/41507235\) | \(1328231520000000\) | \([2]\) | \(491520\) | \(1.6327\) | |
| 92400.ik3 | 92400cq2 | \([0, 1, 0, -11408, 409188]\) | \(10262905636/1334025\) | \(21344400000000\) | \([2, 2]\) | \(245760\) | \(1.2861\) | |
| 92400.ik4 | 92400cq1 | \([0, 1, 0, 1092, 34188]\) | \(35969456/144375\) | \(-577500000000\) | \([2]\) | \(122880\) | \(0.93951\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.ik have rank \(0\).
Complex multiplication
The elliptic curves in class 92400.ik do not have complex multiplication.Modular form 92400.2.a.ik
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.
