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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 414736.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414736.m1 | 414736m2 | \([0, 1, 0, -89784, 10326868]\) | \(-313994137/64\) | \(-16314878132224\) | \([]\) | \(2073600\) | \(1.5328\) | \(\Gamma_0(N)\)-optimal* |
414736.m2 | 414736m1 | \([0, 1, 0, 376, 48628]\) | \(23/4\) | \(-1019679883264\) | \([]\) | \(691200\) | \(0.98348\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414736.m have rank \(0\).
Complex multiplication
The elliptic curves in class 414736.m do not have complex multiplication.Modular form 414736.2.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.