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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 3870.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3870.o1 | 3870r2 | \([1, -1, 1, -2138, 37361]\) | \(1481933914201/53916840\) | \(39305376360\) | \([2]\) | \(4608\) | \(0.80261\) | |
3870.o2 | 3870r1 | \([1, -1, 1, -338, -1519]\) | \(5841725401/1857600\) | \(1354190400\) | \([2]\) | \(2304\) | \(0.45604\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3870.o have rank \(1\).
Complex multiplication
The elliptic curves in class 3870.o do not have complex multiplication.Modular form 3870.2.a.o
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.