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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 50960m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50960.bx1 | 50960m1 | \([0, -1, 0, -23340, 1277312]\) | \(46689225424/3901625\) | \(117509703584000\) | \([2]\) | \(221184\) | \(1.4417\) | \(\Gamma_0(N)\)-optimal |
| 50960.bx2 | 50960m2 | \([0, -1, 0, 24680, 5810400]\) | \(13799183324/129390625\) | \(-15588021904000000\) | \([2]\) | \(442368\) | \(1.7883\) |
Rank
sage: E.rank()
The elliptic curves in class 50960m have rank \(0\).
Complex multiplication
The elliptic curves in class 50960m do not have complex multiplication.Modular form 50960.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
