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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 2240.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2240.m1 | 2240t3 | \([0, 0, 0, -52268, -4599408]\) | \(481927184300808/1225\) | \(40140800\) | \([2]\) | \(3072\) | \(1.1226\) | |
| 2240.m2 | 2240t4 | \([0, 0, 0, -4268, -24208]\) | \(262389836808/144120025\) | \(4722524979200\) | \([4]\) | \(3072\) | \(1.1226\) | |
| 2240.m3 | 2240t2 | \([0, 0, 0, -3268, -71808]\) | \(942344950464/1500625\) | \(6146560000\) | \([2, 2]\) | \(1536\) | \(0.77603\) | |
| 2240.m4 | 2240t1 | \([0, 0, 0, -143, -1808]\) | \(-5053029696/19140625\) | \(-1225000000\) | \([2]\) | \(768\) | \(0.42945\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2240.m have rank \(1\).
Complex multiplication
The elliptic curves in class 2240.m do not have complex multiplication.Modular form 2240.2.a.m
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.
