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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 91200a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 91200.cm4 | 91200a1 | \([0, -1, 0, -9533, 703437]\) | \(-5988775936/9774075\) | \(-156385200000000\) | \([2]\) | \(196608\) | \(1.4146\) | \(\Gamma_0(N)\)-optimal |
| 91200.cm3 | 91200a2 | \([0, -1, 0, -190033, 31929937]\) | \(2964647793616/2030625\) | \(519840000000000\) | \([2, 2]\) | \(393216\) | \(1.7612\) | |
| 91200.cm2 | 91200a3 | \([0, -1, 0, -228033, 18287937]\) | \(1280615525284/601171875\) | \(615600000000000000\) | \([2]\) | \(786432\) | \(2.1077\) | |
| 91200.cm1 | 91200a4 | \([0, -1, 0, -3040033, 2041179937]\) | \(3034301922374404/1425\) | \(1459200000000\) | \([2]\) | \(786432\) | \(2.1077\) |
Rank
sage: E.rank()
The elliptic curves in class 91200a have rank \(1\).
Complex multiplication
The elliptic curves in class 91200a do not have complex multiplication.Modular form 91200.2.a.a
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.
