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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 18150.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18150.m1 | 18150i3 | \([1, 1, 0, -243575, 45991125]\) | \(57736239625/255552\) | \(7073843073000000\) | \([2]\) | \(207360\) | \(1.8936\) | |
18150.m2 | 18150i4 | \([1, 1, 0, -122575, 91850125]\) | \(-7357983625/127552392\) | \(-3530731923811125000\) | \([2]\) | \(414720\) | \(2.2402\) | |
18150.m3 | 18150i1 | \([1, 1, 0, -16700, -790500]\) | \(18609625/1188\) | \(32884601062500\) | \([2]\) | \(69120\) | \(1.3443\) | \(\Gamma_0(N)\)-optimal |
18150.m4 | 18150i2 | \([1, 1, 0, 13550, -3301250]\) | \(9938375/176418\) | \(-4883363257781250\) | \([2]\) | \(138240\) | \(1.6909\) |
Rank
sage: E.rank()
The elliptic curves in class 18150.m have rank \(0\).
Complex multiplication
The elliptic curves in class 18150.m do not have complex multiplication.Modular form 18150.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.