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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 110400m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 110400.bf1 | 110400m1 | \([0, -1, 0, -708, 4662]\) | \(39304000/14283\) | \(14283000000\) | \([2]\) | \(55296\) | \(0.64901\) | \(\Gamma_0(N)\)-optimal |
| 110400.bf2 | 110400m2 | \([0, -1, 0, 2167, 30537]\) | \(17576000/16767\) | \(-1073088000000\) | \([2]\) | \(110592\) | \(0.99559\) |
Rank
sage: E.rank()
The elliptic curves in class 110400m have rank \(1\).
Complex multiplication
The elliptic curves in class 110400m do not have complex multiplication.Modular form 110400.2.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.
