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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 3366m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3366.q4 | 3366m1 | \([1, -1, 1, -59999, -4240569]\) | \(32765849647039657/8229948198912\) | \(5999632237006848\) | \([4]\) | \(21504\) | \(1.7375\) | \(\Gamma_0(N)\)-optimal |
| 3366.q2 | 3366m2 | \([1, -1, 1, -892319, -324184377]\) | \(107784459654566688937/10704361149504\) | \(7803479277988416\) | \([2, 2]\) | \(43008\) | \(2.0841\) | |
| 3366.q1 | 3366m3 | \([1, -1, 1, -14276759, -20759547369]\) | \(441453577446719855661097/4354701912\) | \(3174577693848\) | \([2]\) | \(86016\) | \(2.4306\) | |
| 3366.q3 | 3366m4 | \([1, -1, 1, -824999, -375212937]\) | \(-85183593440646799657/34223681512621656\) | \(-24949063822701187224\) | \([2]\) | \(86016\) | \(2.4306\) |
Rank
sage: E.rank()
The elliptic curves in class 3366m have rank \(0\).
Complex multiplication
The elliptic curves in class 3366m do not have complex multiplication.Modular form 3366.2.a.m
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 Cremona 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 Cremona labels.
