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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 48400.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48400.m1 | 48400co2 | \([0, 1, 0, -20808, -1193612]\) | \(-128667913/4096\) | \(-31719424000000\) | \([]\) | \(124416\) | \(1.3667\) | |
48400.m2 | 48400co1 | \([0, 1, 0, 1192, -5612]\) | \(24167/16\) | \(-123904000000\) | \([]\) | \(41472\) | \(0.81735\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 48400.m have rank \(1\).
Complex multiplication
The elliptic curves in class 48400.m do not have complex multiplication.Modular form 48400.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.