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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 102960.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102960.i1 | 102960dl2 | \([0, 0, 0, -15843, -499358]\) | \(147281603041/49156250\) | \(146779776000000\) | \([2]\) | \(331776\) | \(1.4209\) | |
102960.i2 | 102960dl1 | \([0, 0, 0, 2877, -53822]\) | \(881974079/929500\) | \(-2775472128000\) | \([2]\) | \(165888\) | \(1.0744\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.i have rank \(0\).
Complex multiplication
The elliptic curves in class 102960.i do not have complex multiplication.Modular form 102960.2.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.