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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 5070.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5070.m1 | 5070o2 | \([1, 1, 1, -117036, 15362043]\) | \(16718302693/90\) | \(954404943570\) | \([2]\) | \(24960\) | \(1.4932\) | |
5070.m2 | 5070o1 | \([1, 1, 1, -7186, 246683]\) | \(-3869893/300\) | \(-3181349811900\) | \([2]\) | \(12480\) | \(1.1466\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5070.m have rank \(1\).
Complex multiplication
The elliptic curves in class 5070.m do not have complex multiplication.Modular form 5070.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.