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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 102960di
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102960.o4 | 102960di1 | \([0, 0, 0, -86043, -111791158]\) | \(-23592983745241/1794399750000\) | \(-5358048943104000000\) | \([2]\) | \(1327104\) | \(2.2734\) | \(\Gamma_0(N)\)-optimal |
102960.o3 | 102960di2 | \([0, 0, 0, -4046043, -3111095158]\) | \(2453170411237305241/19353090685500\) | \(57788019137452032000\) | \([2]\) | \(2654208\) | \(2.6200\) | |
102960.o2 | 102960di3 | \([0, 0, 0, -20444043, -35580060358]\) | \(-316472948332146183241/7074906009600\) | \(-21125556146169446400\) | \([2]\) | \(3981312\) | \(2.8228\) | |
102960.o1 | 102960di4 | \([0, 0, 0, -327106443, -2277098206918]\) | \(1296294060988412126189641/647824320\) | \(1934393054330880\) | \([2]\) | \(7962624\) | \(3.1693\) |
Rank
sage: E.rank()
The elliptic curves in class 102960di have rank \(2\).
Complex multiplication
The elliptic curves in class 102960di do not have complex multiplication.Modular form 102960.2.a.di
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.