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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 75150l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75150.o2 | 75150l1 | \([1, -1, 0, -11367, 580041]\) | \(-14260515625/4382748\) | \(-49922238937500\) | \([2]\) | \(221184\) | \(1.3421\) | \(\Gamma_0(N)\)-optimal |
75150.o1 | 75150l2 | \([1, -1, 0, -193617, 32838291]\) | \(70470585447625/4518018\) | \(51463048781250\) | \([2]\) | \(442368\) | \(1.6887\) |
Rank
sage: E.rank()
The elliptic curves in class 75150l have rank \(1\).
Complex multiplication
The elliptic curves in class 75150l do not have complex multiplication.Modular form 75150.2.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 Cremona 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 Cremona labels.