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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 11760j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11760.z4 | 11760j1 | \([0, -1, 0, 425, -27950]\) | \(4499456/180075\) | \(-338970298800\) | \([2]\) | \(12288\) | \(0.89228\) | \(\Gamma_0(N)\)-optimal |
11760.z3 | 11760j2 | \([0, -1, 0, -11580, -455328]\) | \(5702413264/275625\) | \(8301313440000\) | \([2, 2]\) | \(24576\) | \(1.2389\) | |
11760.z1 | 11760j3 | \([0, -1, 0, -183080, -30090528]\) | \(5633270409316/14175\) | \(1707698764800\) | \([2]\) | \(49152\) | \(1.5854\) | |
11760.z2 | 11760j4 | \([0, -1, 0, -32160, 1635600]\) | \(30534944836/8203125\) | \(988251600000000\) | \([4]\) | \(49152\) | \(1.5854\) |
Rank
sage: E.rank()
The elliptic curves in class 11760j have rank \(1\).
Complex multiplication
The elliptic curves in class 11760j do not have complex multiplication.Modular form 11760.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.