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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 377520v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.v4 | 377520v1 | \([0, -1, 0, -13471, -225674]\) | \(9538484224/4712565\) | \(133577541823440\) | \([2]\) | \(1228800\) | \(1.4036\) | \(\Gamma_0(N)\)-optimal |
| 377520.v2 | 377520v2 | \([0, -1, 0, -115716, 15029280]\) | \(377843214544/4601025\) | \(2086655091206400\) | \([2, 2]\) | \(2457600\) | \(1.7501\) | |
| 377520.v1 | 377520v3 | \([0, -1, 0, -1846016, 966002160]\) | \(383507853966436/57915\) | \(105062354242560\) | \([2]\) | \(4915200\) | \(2.0967\) | |
| 377520.v3 | 377520v4 | \([0, -1, 0, -21336, 38737536]\) | \(-592143556/356874375\) | \(-647398118040960000\) | \([2]\) | \(4915200\) | \(2.0967\) |
Rank
sage: E.rank()
The elliptic curves in class 377520v have rank \(0\).
Complex multiplication
The elliptic curves in class 377520v do not have complex multiplication.Modular form 377520.2.a.v
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.
