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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 53040.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53040.m1 | 53040a1 | \([0, -1, 0, -281016, -57158784]\) | \(2396726313900986596/4154072495625\) | \(4253770235520000\) | \([2]\) | \(368640\) | \(1.8928\) | \(\Gamma_0(N)\)-optimal |
| 53040.m2 | 53040a2 | \([0, -1, 0, -193136, -93646560]\) | \(-389032340685029858/1627263833203125\) | \(-3332636330400000000\) | \([2]\) | \(737280\) | \(2.2393\) |
Rank
sage: E.rank()
The elliptic curves in class 53040.m have rank \(1\).
Complex multiplication
The elliptic curves in class 53040.m do not have complex multiplication.Modular form 53040.2.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 LMFDB 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 LMFDB labels.
