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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 76440i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76440.l2 | 76440i1 | \([0, -1, 0, -66656, 9223740]\) | \(-792621148/426465\) | \(-17622426633477120\) | \([2]\) | \(430080\) | \(1.8212\) | \(\Gamma_0(N)\)-optimal |
| 76440.l1 | 76440i2 | \([0, -1, 0, -1177976, 492425676]\) | \(2187364176254/342225\) | \(28282906942617600\) | \([2]\) | \(860160\) | \(2.1678\) |
Rank
sage: E.rank()
The elliptic curves in class 76440i have rank \(1\).
Complex multiplication
The elliptic curves in class 76440i do not have complex multiplication.Modular form 76440.2.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 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.
