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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 92400en
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.dr3 | 92400en1 | \([0, -1, 0, -81408, -8906688]\) | \(932288503609/779625\) | \(49896000000000\) | \([2]\) | \(442368\) | \(1.5563\) | \(\Gamma_0(N)\)-optimal |
92400.dr2 | 92400en2 | \([0, -1, 0, -99408, -4658688]\) | \(1697509118089/833765625\) | \(53361000000000000\) | \([2, 2]\) | \(884736\) | \(1.9029\) | |
92400.dr4 | 92400en3 | \([0, -1, 0, 362592, -36074688]\) | \(82375335041831/56396484375\) | \(-3609375000000000000\) | \([2]\) | \(1769472\) | \(2.2495\) | |
92400.dr1 | 92400en4 | \([0, -1, 0, -849408, 298341312]\) | \(1058993490188089/13182390375\) | \(843672984000000000\) | \([4]\) | \(1769472\) | \(2.2495\) |
Rank
sage: E.rank()
The elliptic curves in class 92400en have rank \(0\).
Complex multiplication
The elliptic curves in class 92400en do not have complex multiplication.Modular form 92400.2.a.en
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.