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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 1872.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1872.m1 | 1872n2 | \([0, 0, 0, -30627, -2263518]\) | \(-1064019559329/125497034\) | \(-374732135571456\) | \([]\) | \(4704\) | \(1.5322\) | |
1872.m2 | 1872n1 | \([0, 0, 0, -387, 4482]\) | \(-2146689/1664\) | \(-4968677376\) | \([]\) | \(672\) | \(0.55929\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1872.m have rank \(1\).
Complex multiplication
The elliptic curves in class 1872.m do not have complex multiplication.Modular form 1872.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.