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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 76440l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76440.q3 | 76440l1 | \([0, -1, 0, -53916, -4223820]\) | \(575514878416/74972625\) | \(2258036315808000\) | \([2]\) | \(442368\) | \(1.6745\) | \(\Gamma_0(N)\)-optimal |
76440.q2 | 76440l2 | \([0, -1, 0, -219536, 35326236]\) | \(9713030100484/1164515625\) | \(140292197136000000\) | \([2, 2]\) | \(884736\) | \(2.0210\) | |
76440.q4 | 76440l3 | \([0, -1, 0, 315544, 180225900]\) | \(14420619677518/66650390625\) | \(-16059088500000000000\) | \([2]\) | \(1769472\) | \(2.3676\) | |
76440.q1 | 76440l4 | \([0, -1, 0, -3404536, 2418980236]\) | \(18112543427820242/316031625\) | \(76146287922432000\) | \([2]\) | \(1769472\) | \(2.3676\) |
Rank
sage: E.rank()
The elliptic curves in class 76440l have rank \(1\).
Complex multiplication
The elliptic curves in class 76440l do not have complex multiplication.Modular form 76440.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.