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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 176605g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176605.d3 | 176605g1 | \([1, -1, 1, -166027153, -823369737888]\) | \(104857852278310619039721/47155625\) | \(227611195150625\) | \([2]\) | \(10174464\) | \(2.9983\) | \(\Gamma_0(N)\)-optimal |
| 176605.d2 | 176605g2 | \([1, -1, 1, -166027998, -823360937044]\) | \(104859453317683374662841/2223652969140625\) | \(10733148164324691015625\) | \([2, 2]\) | \(20348928\) | \(3.3449\) | |
| 176605.d1 | 176605g3 | \([1, -1, 1, -171837373, -762643673294]\) | \(116256292809537371612841/15216540068579856875\) | \(73447332551881870382961875\) | \([2]\) | \(40697856\) | \(3.6914\) | |
| 176605.d4 | 176605g4 | \([1, -1, 1, -160232143, -883514956918]\) | \(-94256762600623910012361/15323275604248046875\) | \(-73962524596064910888671875\) | \([2]\) | \(40697856\) | \(3.6914\) |
Rank
sage: E.rank()
The elliptic curves in class 176605g have rank \(0\).
Complex multiplication
The elliptic curves in class 176605g do not have complex multiplication.Modular form 176605.2.a.g
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.
