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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 479808.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
479808.m1 | 479808m2 | \([0, 0, 0, -219324, 39522224]\) | \(40685771728/14739\) | \(422676056162304\) | \([]\) | \(4313088\) | \(1.7751\) | \(\Gamma_0(N)\)-optimal* |
479808.m2 | 479808m1 | \([0, 0, 0, -7644, -188944]\) | \(1722448/459\) | \(13162922164224\) | \([]\) | \(1437696\) | \(1.2258\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 479808.m have rank \(3\).
Complex multiplication
The elliptic curves in class 479808.m do not have complex multiplication.Modular form 479808.2.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.