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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 117600fe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117600.dh3 | 117600fe1 | \([0, -1, 0, -24311758, 46137119512]\) | \(13507798771700416/3544416225\) | \(416997024455025000000\) | \([2, 2]\) | \(8847360\) | \(2.9414\) | \(\Gamma_0(N)\)-optimal |
| 117600.dh4 | 117600fe2 | \([0, -1, 0, -21335008, 57853607512]\) | \(-1141100604753992/875529151875\) | \(-824041033511535000000000\) | \([2]\) | \(17694720\) | \(3.2879\) | |
| 117600.dh2 | 117600fe3 | \([0, -1, 0, -27313008, 34030077012]\) | \(2394165105226952/854262178245\) | \(804024728066768040000000\) | \([2]\) | \(17694720\) | \(3.2879\) | |
| 117600.dh1 | 117600fe4 | \([0, -1, 0, -388963633, 2952777215137]\) | \(864335783029582144/59535\) | \(448270925760000000\) | \([2]\) | \(17694720\) | \(3.2879\) |
Rank
sage: E.rank()
The elliptic curves in class 117600fe have rank \(1\).
Complex multiplication
The elliptic curves in class 117600fe do not have complex multiplication.Modular form 117600.2.a.fe
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
