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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 130536.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 130536.m1 | 130536d2 | \([0, 0, 0, -1448391, -537459734]\) | \(15304721495632/3173346477\) | \(69674398187854263552\) | \([2]\) | \(2654208\) | \(2.5227\) | |
| 130536.m2 | 130536d1 | \([0, 0, 0, -1366806, -615014435]\) | \(205782571927552/12678309\) | \(17397910140310224\) | \([2]\) | \(1327104\) | \(2.1761\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 130536.m have rank \(0\).
Complex multiplication
The elliptic curves in class 130536.m do not have complex multiplication.Modular form 130536.2.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.
