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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 13005.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13005.l1 | 13005o2 | \([0, 0, 1, -2146692, 1210596507]\) | \(17968412610002944/158203125\) | \(9632483455078125\) | \([3]\) | \(165888\) | \(2.2335\) | |
13005.l2 | 13005o1 | \([0, 0, 1, -39882, -187200]\) | \(115220905984/66430125\) | \(4044718332721125\) | \([]\) | \(55296\) | \(1.6842\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13005.l have rank \(0\).
Complex multiplication
The elliptic curves in class 13005.l do not have complex multiplication.Modular form 13005.2.a.l
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.