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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 28880m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28880.f2 | 28880m1 | \([0, 1, 0, -9398755, -11102802900]\) | \(-121981271658244096/115966796875\) | \(-87292162011718750000\) | \([2]\) | \(1612800\) | \(2.7482\) | \(\Gamma_0(N)\)-optimal |
| 28880.f1 | 28880m2 | \([0, 1, 0, -150414380, -710089052900]\) | \(31248575021659890256/28203125\) | \(339671260820000000\) | \([2]\) | \(3225600\) | \(3.0948\) |
Rank
sage: E.rank()
The elliptic curves in class 28880m have rank \(1\).
Complex multiplication
The elliptic curves in class 28880m do not have complex multiplication.Modular form 28880.2.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.
