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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 76440.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76440.t1 | 76440u4 | \([0, -1, 0, -612320, 184626492]\) | \(210751929444676/1404585\) | \(169213973160960\) | \([2]\) | \(589824\) | \(1.9125\) | |
| 76440.t2 | 76440u3 | \([0, -1, 0, -128200, -14382500]\) | \(1934207124196/373156875\) | \(44955169983360000\) | \([2]\) | \(589824\) | \(1.9125\) | |
| 76440.t3 | 76440u2 | \([0, -1, 0, -39020, 2775732]\) | \(218156637904/16769025\) | \(505051909689600\) | \([2, 2]\) | \(294912\) | \(1.5659\) | |
| 76440.t4 | 76440u1 | \([0, -1, 0, 2385, 192060]\) | \(796706816/8996715\) | \(-16935272368560\) | \([4]\) | \(147456\) | \(1.2193\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76440.t have rank \(0\).
Complex multiplication
The elliptic curves in class 76440.t do not have complex multiplication.Modular form 76440.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
