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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 5040v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5040.e4 | 5040v1 | \([0, 0, 0, -348, -2497]\) | \(10788913152/8575\) | \(3704400\) | \([2]\) | \(1152\) | \(0.19075\) | \(\Gamma_0(N)\)-optimal |
5040.e3 | 5040v2 | \([0, 0, 0, -423, -1342]\) | \(1210991472/588245\) | \(4065949440\) | \([2]\) | \(2304\) | \(0.53732\) | |
5040.e2 | 5040v3 | \([0, 0, 0, -1188, 12987]\) | \(588791808/109375\) | \(34445250000\) | \([2]\) | \(3456\) | \(0.74005\) | |
5040.e1 | 5040v4 | \([0, 0, 0, -18063, 934362]\) | \(129348709488/6125\) | \(30862944000\) | \([2]\) | \(6912\) | \(1.0866\) |
Rank
sage: E.rank()
The elliptic curves in class 5040v have rank \(0\).
Complex multiplication
The elliptic curves in class 5040v do not have complex multiplication.Modular form 5040.2.a.v
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 Cremona 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 Cremona labels.