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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 3360.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3360.q1 | 3360u2 | \([0, 1, 0, -324016, -71098216]\) | \(7347751505995469192/72930375\) | \(37340352000\) | \([2]\) | \(15360\) | \(1.6049\) | |
3360.q2 | 3360u3 | \([0, 1, 0, -29016, -67716]\) | \(5276930158229192/3050936350875\) | \(1562079411648000\) | \([2]\) | \(15360\) | \(1.6049\) | |
3360.q3 | 3360u1 | \([0, 1, 0, -20266, -1114216]\) | \(14383655824793536/45209390625\) | \(2893401000000\) | \([2, 2]\) | \(7680\) | \(1.2583\) | \(\Gamma_0(N)\)-optimal |
3360.q4 | 3360u4 | \([0, 1, 0, -11761, -2048065]\) | \(-43927191786304/415283203125\) | \(-1701000000000000\) | \([2]\) | \(15360\) | \(1.6049\) |
Rank
sage: E.rank()
The elliptic curves in class 3360.q have rank \(0\).
Complex multiplication
The elliptic curves in class 3360.q do not have complex multiplication.Modular form 3360.2.a.q
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.