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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 162240di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.g2 | 162240di1 | \([0, -1, 0, -13121, 1269345]\) | \(-1735192372/3796875\) | \(-546683904000000\) | \([2]\) | \(921600\) | \(1.5167\) | \(\Gamma_0(N)\)-optimal |
| 162240.g1 | 162240di2 | \([0, -1, 0, -273121, 54985345]\) | \(7824392006186/7381125\) | \(2125507018752000\) | \([2]\) | \(1843200\) | \(1.8632\) |
Rank
sage: E.rank()
The elliptic curves in class 162240di have rank \(1\).
Complex multiplication
The elliptic curves in class 162240di do not have complex multiplication.Modular form 162240.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
