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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 60984.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60984.i1 | 60984v2 | \([0, 0, 0, -24820851, 33383409950]\) | \(1278763167594532/375974556419\) | \(497212515096700767243264\) | \([2]\) | \(5529600\) | \(3.2528\) | |
| 60984.i2 | 60984v1 | \([0, 0, 0, 4168329, 3472374026]\) | \(24226243449392/29774625727\) | \(-9843961706338262646528\) | \([2]\) | \(2764800\) | \(2.9062\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 60984.i have rank \(1\).
Complex multiplication
The elliptic curves in class 60984.i do not have complex multiplication.Modular form 60984.2.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.
