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SageMath
E = EllipticCurve("di1")
E.isogeny_class()
Elliptic curves in class 187200di
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187200.ef2 | 187200di1 | \([0, 0, 0, -1769700, 1091464000]\) | \(-13137573612736/3427734375\) | \(-159924375000000000000\) | \([2]\) | \(4423680\) | \(2.5937\) | \(\Gamma_0(N)\)-optimal |
| 187200.ef1 | 187200di2 | \([0, 0, 0, -29894700, 62910214000]\) | \(7916055336451592/385003125\) | \(143701646400000000000\) | \([2]\) | \(8847360\) | \(2.9403\) |
Rank
sage: E.rank()
The elliptic curves in class 187200di have rank \(1\).
Complex multiplication
The elliptic curves in class 187200di do not have complex multiplication.Modular form 187200.2.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.
