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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 277248m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277248.m2 | 277248m1 | \([0, 1, 0, -1203, 68697]\) | \(-8000/81\) | \(-1951086776832\) | \([2]\) | \(442368\) | \(1.0405\) | \(\Gamma_0(N)\)-optimal |
| 277248.m1 | 277248m2 | \([0, 1, 0, -33693, 2362491]\) | \(2744000/9\) | \(13874394857472\) | \([2]\) | \(884736\) | \(1.3871\) |
Rank
sage: E.rank()
The elliptic curves in class 277248m have rank \(0\).
Complex multiplication
The elliptic curves in class 277248m do not have complex multiplication.Modular form 277248.2.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.
