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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 327990.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
327990.m1 | 327990m2 | \([1, 0, 1, -38704, -2628628]\) | \(10779215329/1232010\) | \(732828279705210\) | \([2]\) | \(2376192\) | \(1.5846\) | |
327990.m2 | 327990m1 | \([1, 0, 1, 3346, -206548]\) | \(6967871/35100\) | \(-20878298567100\) | \([2]\) | \(1188096\) | \(1.2380\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 327990.m have rank \(0\).
Complex multiplication
The elliptic curves in class 327990.m do not have complex multiplication.Modular form 327990.2.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.