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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 102960.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102960.j1 | 102960dy4 | \([0, 0, 0, -11807643, -9439421942]\) | \(60971359344939402841/22393337786551875\) | \(66866148337239313920000\) | \([4]\) | \(11010048\) | \(3.0800\) | |
102960.j2 | 102960dy2 | \([0, 0, 0, -10457643, -13013411942]\) | \(42358217070122052841/12149581640625\) | \(36278456385600000000\) | \([2, 2]\) | \(5505024\) | \(2.7334\) | |
102960.j3 | 102960dy1 | \([0, 0, 0, -10456923, -13015293878]\) | \(42349468688699229721/3485625\) | \(10408020480000\) | \([2]\) | \(2752512\) | \(2.3868\) | \(\Gamma_0(N)\)-optimal |
102960.j4 | 102960dy3 | \([0, 0, 0, -9119163, -16466958038]\) | \(-28086729490688202361/22976531982421875\) | \(-68607556875000000000000\) | \([2]\) | \(11010048\) | \(3.0800\) |
Rank
sage: E.rank()
The elliptic curves in class 102960.j have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.j do not have complex multiplication.Modular form 102960.2.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 LMFDB 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 LMFDB labels.