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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 64400m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64400.f2 | 64400m1 | \([0, 1, 0, -107408, 8297188]\) | \(8564808605476/3081640625\) | \(49306250000000000\) | \([2]\) | \(589824\) | \(1.9038\) | \(\Gamma_0(N)\)-optimal |
| 64400.f1 | 64400m2 | \([0, 1, 0, -732408, -235452812]\) | \(1357792998752738/38897700625\) | \(1244726420000000000\) | \([2]\) | \(1179648\) | \(2.2504\) |
Rank
sage: E.rank()
The elliptic curves in class 64400m have rank \(0\).
Complex multiplication
The elliptic curves in class 64400m do not have complex multiplication.Modular form 64400.2.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.
