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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 15030.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15030.i1 | 15030i2 | \([1, -1, 1, -223103, -40504913]\) | \(-62394574179743883/167000\) | \(-3287061000\) | \([]\) | \(51840\) | \(1.4864\) | |
15030.i2 | 15030i1 | \([1, -1, 1, -2663, -58849]\) | \(-77325109990227/11923105280\) | \(-321923842560\) | \([3]\) | \(17280\) | \(0.93707\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15030.i have rank \(1\).
Complex multiplication
The elliptic curves in class 15030.i do not have complex multiplication.Modular form 15030.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.