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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 480.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
480.e1 | 480c3 | \([0, 1, 0, -81, 255]\) | \(14526784/15\) | \(61440\) | \([2]\) | \(64\) | \(-0.16327\) | |
480.e2 | 480c2 | \([0, 1, 0, -56, -180]\) | \(38614472/405\) | \(207360\) | \([2]\) | \(64\) | \(-0.16327\) | |
480.e3 | 480c1 | \([0, 1, 0, -6, 0]\) | \(438976/225\) | \(14400\) | \([2, 2]\) | \(32\) | \(-0.50984\) | \(\Gamma_0(N)\)-optimal |
480.e4 | 480c4 | \([0, 1, 0, 24, 24]\) | \(2863288/1875\) | \(-960000\) | \([2]\) | \(64\) | \(-0.16327\) |
Rank
sage: E.rank()
The elliptic curves in class 480.e have rank \(0\).
Complex multiplication
The elliptic curves in class 480.e do not have complex multiplication.Modular form 480.2.a.e
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.