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SageMath
E = EllipticCurve("ii1")
E.isogeny_class()
Elliptic curves in class 277200.ii
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.ii1 | 277200ii4 | \([0, 0, 0, -50878875, -139676669750]\) | \(312196988566716625/25367712678\) | \(1183556002704768000000\) | \([2]\) | \(15925248\) | \(3.0887\) | |
| 277200.ii2 | 277200ii3 | \([0, 0, 0, -2962875, -2493161750]\) | \(-61653281712625/21875235228\) | \(-1020610974797568000000\) | \([2]\) | \(7962624\) | \(2.7422\) | |
| 277200.ii3 | 277200ii2 | \([0, 0, 0, -1306875, 288414250]\) | \(5290763640625/2291573592\) | \(106915657508352000000\) | \([2]\) | \(5308416\) | \(2.5394\) | |
| 277200.ii4 | 277200ii1 | \([0, 0, 0, 277125, 33390250]\) | \(50447927375/39517632\) | \(-1843734638592000000\) | \([2]\) | \(2654208\) | \(2.1928\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277200.ii have rank \(0\).
Complex multiplication
The elliptic curves in class 277200.ii do not have complex multiplication.Modular form 277200.2.a.ii
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
