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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 118580.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
118580.v1 | 118580a1 | \([0, 1, 0, -120556, -16161356]\) | \(-177953104/125\) | \(-136112574752000\) | \([]\) | \(466560\) | \(1.6483\) | \(\Gamma_0(N)\)-optimal |
118580.v2 | 118580a2 | \([0, 1, 0, 116604, -68431420]\) | \(161017136/1953125\) | \(-2126758980500000000\) | \([]\) | \(1399680\) | \(2.1976\) |
Rank
sage: E.rank()
The elliptic curves in class 118580.v have rank \(1\).
Complex multiplication
The elliptic curves in class 118580.v do not have complex multiplication.Modular form 118580.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.