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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 277200.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.i1 | 277200i2 | \([0, 0, 0, -243435, 10591450]\) | \(4274401176989/2343775203\) | \(874809406969344000\) | \([2]\) | \(2949120\) | \(2.1334\) | |
| 277200.i2 | 277200i1 | \([0, 0, 0, -146235, -21387350]\) | \(926574216749/6792093\) | \(2535135128064000\) | \([2]\) | \(1474560\) | \(1.7868\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277200.i have rank \(0\).
Complex multiplication
The elliptic curves in class 277200.i do not have complex multiplication.Modular form 277200.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
